Change search
Refine search result
1 - 21 of 21
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Baghdari, Samaneh
    et al.
    Isfahan University of Technology, Iran.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Pure semisimple and Kothe group rings2023In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 51, no 7, p. 2779-2790Article in journal (Refereed)
    Abstract [en]

    In this article, we provide a complete characterization of abelian group rings which are Kothe rings. We also provide characterizations of (possibly non-abelian) group rings over division rings which are Kothe rings, both in characteristic zero and in prime characteristic, and prove a Maschke type result for pure semisimplicity of group rings. Furthermore, we illustrate our results by several examples.Communicated by Eric Jespers

    Download full text (pdf)
    fulltext
  • 2.
    Bagio, Dirceu
    et al.
    Universidade Federal de Santa Catarina, Brazil.
    Gonçalves, Daniel
    Universidade Federal de Santa Catarina, Brazil.
    Moreira, Paula Savana Estácio
    Universidade Federal de Santa Catarina, Brazil.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras2024In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337Article in journal (Refereed)
    Abstract [en]

    Given a partial action α of a groupoid G on a ring R, we study the associated partial skew groupoid ring R ⋊ α G {R\rtimes_{\alpha}G}, which carries a natural G-grading. We show that there is a one-to-one correspondence between the G-invariant ideals of R and the graded ideals of the G-graded ring R ⋊ α G {R\rtimes_{\alpha}G}. We provide sufficient conditions for primeness, and necessary and sufficient conditions for simplicity of R ⋊ α G {R\rtimes_{\alpha}G}. We show that every ideal of R ⋊ α G {R\rtimes_{\alpha}G} is graded if and only if α has the residual intersection property. Furthermore, if α is induced by a topological partial action θ, then we prove that minimality of θ is equivalent to G-simplicity of R, topological transitivity of θ is equivalent to G-primeness of R, and topological freeness of θ on every closed invariant subset of the underlying topological space is equivalent to α having the residual intersection property. As an application, we characterize condition (K) for an ultragraph in terms of topological properties of the associated partial action and in terms of algebraic properties of the associated ultragraph algebra. © 2024 Walter de Gruyter GmbH, Berlin/Boston 2024.

  • 3.
    Beuter, Viviane
    et al.
    Universidade Federal de Santa Catarina, BRA.
    Gonçalves, Daniel
    Universidade Federal de Santa Catarina, BRA.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Royer, Danilo
    Universidade Federal de Santa Catarina, BRA.
    Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics2019In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 31, no 3, p. 543-562Article in journal (Refereed)
    Abstract [en]

    Given a partial action π of an inverse semigroup S on a ring A {\mathcal{A}}, one may construct its associated skew inverse semigroup ring A π S {\mathcal{A}\rtimes-{\pi}S}. Our main result asserts that, when A {\mathcal{A}} is commutative, the ring A π S {\mathcal{A}\rtimes-{\pi}S} is simple if, and only if, A {\mathcal{A}} is a maximal commutative subring of A π S {\mathcal{A}\rtimes-{\pi}S} and A {\mathcal{A}} is S-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. Furthermore, we use our result to present a new proof of the simplicity criterion for a Steinberg algebra A R (g) {A-{R}(\mathcal{G})} associated with a Hausdorff and ample groupoid g {\mathcal{G}}. © 2018 Walter de Gruyter GmbH, Berlin/Boston.

  • 4.
    Lorensen, Karl
    et al.
    Pennsylvania State University, United States.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Generating numbers of rings graded by amenable and supramenable groups2024In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 109, no 1, article id e12826Article in journal (Refereed)
    Abstract [en]

    A ring 𝑅 has unbounded generating number (UGN) if,for every positive integer 𝑛, there is no 𝑅-module epimorphism 𝑅𝑛 → 𝑅𝑛+1. For a ring 𝑅 = ⨁g∈𝐺 𝑅g gradedby a group 𝐺 such that the base ring 𝑅1 has UGN, weidentify several sets of conditions under which 𝑅 mustalso have UGN. The most important of these are: (1)𝐺 is amenable, and there is a positive integer 𝑟 suchthat, for every g ∈ 𝐺, 𝑅g ≅ (𝑅1)𝑖 as 𝑅1-modules for some𝑖 = 1, … , 𝑟; (2) 𝐺 is supramenable, and there is a positive integer 𝑟 such that, for every g ∈ 𝐺, 𝑅g ≅ (𝑅1)𝑖 as𝑅1-modules for some 𝑖 = 0, … , 𝑟. The pair of conditions(1) leads to three different ring-theoretic characterizations of the property of amenability for groups. We alsoconsider rings that do not have UGN; for such a ring𝑅, the smallest positive integer 𝑛 such that there is an𝑅-module epimorphism 𝑅𝑛 → 𝑅𝑛+1 is called the generating number of 𝑅, denoted gn(𝑅). If 𝑅 has UGN, then wedefine gn(𝑅) ∶= ℵ0. We describe several classes of examples of a ring 𝑅 graded by an amenable group 𝐺 such thatgn(𝑅) ≠ gn(𝑅1).

    MSC 2020

    16P99, 16S35, 16W50, 20F65, 43A07 (primary), 16D90 (secondary)

    Download full text (pdf)
    fulltext
  • 5.
    Lundstrom, Patrik
    et al.
    University West.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    SIMPLICITY OF LEAVITT PATH ALGEBRAS VIA GRADED RING THEORY2023In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 108, no 3, p. 428-437Article in journal (Refereed)
    Abstract [en]

    Suppose that R is an associative unital ring and that E= (E-0, E-1, r, s) is a directed graph. Using results from graded ring theory, we show that the associated Leavitt path algebra L-R(E) is simple if and only if R is simple, E-0 has no nontrivial hereditary and saturated subset, and every cycle in E has an exit. We also give a complete description of the centre of a simple Leavitt path algebra.

    Download full text (pdf)
    fulltext
  • 6.
    Lundstrom, Patrik
    et al.
    University West.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Richter, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    NON-UNITAL ORE EXTENSIONS2023In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 172, no 2, p. 217-229Article in journal (Refereed)
    Abstract [en]

    We study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings R[x; delta], under the hy-pothesis that R is s-unital and ker(delta) contains a non-zero idempotent. This result gener-alizes a result by oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.

  • 7.
    Lundström, Patrik
    et al.
    University West, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Strongly graded leavitt path algebras2022In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 21, no 07, article id 2250141Article in journal (Refereed)
    Abstract [en]

    Let R be a unital ring, let E be a directed graph and recall that the Leavitt path algebra LR(E) carries a natural-gradation. We show that LR(E) is strongly-graded if and only if E is row-finite, has no sink, and satisfies Condition (Y). Our result generalizes a recent result by Clark, Hazrat and Rigby, and the proof is short and self-contained. © 2022 World Scientific Publishing Company

  • 8.
    Lännström, Daniel
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Graded von Neumann regularity of rings graded by semigroups2022In: Beitraege zur Algebra und Geometrie, ISSN 0138-4821, E-ISSN 2191-0383Article in journal (Refereed)
    Abstract [en]

    In this article, we give a complete characterization of semigroup graded rings which are graded von Neumann regular. We also demonstrate our results by applying them to several classes of examples, including matrix rings and groupoid graded rings. © 2022, The Author(s).

    Download full text (pdf)
    fulltext
  • 9.
    Lännström, Daniel
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Wagner, Stefan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Lundström, Patrik
    University West, SWE.
    Prime group graded rings with applications to partial crossed products and Leavitt path algebrasManuscript (preprint) (Other academic)
    Abstract [en]

    In this article we generalize a classical result by Passman on primeness of unital strongly group graded rings to the class of nearly epsilon-strongly group graded rings which are not necessarily unital. Using this result, we obtain (i) a characterization of prime s-unital strongly group graded rings, and, in particular, of infinite matrix rings and of group rings over s-unital rings; (ii) characterizations of prime s-unital partial skew group rings and of prime unital partial crossed products; (iii) a generalization of the well-known characterization of prime Leavitt path algebras, by Abrams, Bell and Rangaswamy.

  • 10.
    Mai Hoang, Bien
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Quasi-duo differential polynomial rings2018In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 17, no 4, article id 1850072Article in journal (Refereed)
    Abstract [en]

    In this article we give a characterization of left (right) quasi-duo differential polynomial rings. We provide non-trivial examples of such rings and give a complete description of the maximal ideals of an arbitrary quasi-duo differential polynomial ring. Moreover, we show that there is no left (right) quasi-duo differential polynomial ring in several indeterminates.

  • 11.
    Nystedt, Patrik
    et al.
    Högskolan Väst, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Group gradations on Leavitt path algebras2020In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 19, no 9, article id 2050165Article in journal (Refereed)
    Abstract [en]

    Given a directed graph E and an associative unital ring R one may define the Leavitt path algebra with coefficients in R, denoted by LR(E). For an arbitrary group G, LR(E) can be viewed as a G-graded ring. In this paper, we show that LR(E) is always nearly epsilon-strongly G-graded. We also show that if E is finite, then LR(E) is epsilon-strongly G-graded. We present a new proof of Hazrat's characterization of strongly g-graded Leavitt path algebras, when E is finite. Moreover, if E is row-finite and has no source, then we show that LR(E) is strongly-graded if and only if E has no sink. We also use a result concerning Frobenius epsilon-strongly G-graded rings, where G is finite, to obtain criteria which ensure that LR(E) is Frobenius over its identity component. © 2020 World Scientific Publishing Company.

  • 12.
    Nystedt, Patrik
    et al.
    University West, Sweden.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Simple graded rings, non-associative crossed products and Cayley-Dickson doublings2020In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 19, no 12, article id 2050231Article in journal (Refereed)
    Abstract [en]

    We show that if a non-associative unital ring is graded by a hypercentral group, then the ring is simple if and only if it is graded simple and the center of the ring is a field. Thereby, we extend a result by Jespers from the associative case to the non-associative situation. By applying this result to non-associative crossed products, we obtain non-associative analogues of results by Bell, Jordan and Voskoglou. We also apply this result to Cayley-Dickson doublings, thereby obtaining a new proof of a classical result by McCrimmon.

  • 13.
    Nystedt, Patrik
    et al.
    Univ West, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Pinedo, Hector
    Univ Ind Santander, COL.
    EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY2020In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 62, no 1, p. 233-259, article id PII S0017089519000065Article in journal (Refereed)
    Abstract [en]

    We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

  • 14.
    Nystedt, Patrik
    et al.
    University West, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Pinedo, Héctor
    Industrial University of Santander, COL.
    Artinian and noetherian partial skew groupoid rings2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 503, p. 433-452Article in journal (Refereed)
    Abstract [en]

    Let α={α_g : R_{g^{−1}}→R_g}_{g∈mor(G)} be a partial action of a groupoid G on a (not necessarily associative) ring R and let S=R⋆G be the associated partial skew groupoid ring. We show that if α is global and unital, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). We use this result to prove that if α is unital and R is alternative, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). This result applies to partial skew group rings, in particular. Both of the above results generalize a theorem by J. K. Park for classical skew group rings, i.e. the case when R is unital and associative, and G is a group which acts globally on R. We provide two additional applications of our main results. Firstly, we generalize I. G. Connell's classical result for group rings by giving a characterization of artinian (not necessarily associative) groupoid rings. This result is in turn applied to partial group algebras. Secondly, we give a characterization of artinian Leavitt path algebras. At the end of the article, we relate noetherian and artinian properties of partial skew groupoid rings to those of global skew groupoid rings, as well as establish two Maschke-type results, thereby generalizing results by M. Ferrero and J. Lazzarin for partial skew group rings to the case of partial skew groupoid rings.

  • 15.
    Nystedt, Patrik
    et al.
    University West, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Pinedo, Héctor
    Industrial University of Santander, COL.
    Epsilon-strongly graded rings, separability and semisimplicity2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 514, no Nov., p. 1-24Article in journal (Refereed)
    Abstract [en]

    We introduce the class of epsilon-strongly graded rings and show that it properly contains both the collection of strongly graded rings and the family of unital partial crossed products. We determine when epsilon-strongly graded rings are separable over their principal components. Thereby, we simultaneously generalize a result for strongly group-graded rings by Nastasescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the family of unital partial crossed products appear in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the family of strongly graded rings. Thereby, we obtain, in the special case of unital partial crossed products, a short proof of a general result by Dokuchaev, Exel and Simon concerning when graded rings can be presented as partial crossed products.

  • 16.
    Nystedt, Patrik
    et al.
    Högskolan Väst, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden..
    Richter, Johan
    Mälardalens högskola, SWE.
    NON-ASSOCIATIVE ORE EXTENSIONS2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed)
    Abstract [en]

    We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R -> R satisfying sigma(1) = 1 and delta(1) = 0. In the special case when delta is either left or right R-delta-linear, where R-delta = ker(delta), and R is delta-simple, i.e. {0} and R are the only delta-invariant ideals of R, we determine the ideal structure of the non-associative differential polynomial ring D = R[X; id(R),delta]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = R-delta[p] for a monic p is an element of R-delta [X], unique up to addition of elements from Z(R)(delta) . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is delta-simple and Z(D) equals the field R-delta boolean AND Z(R). This provides us with a non-associative generalization of a result by Oinert, Richter and Silve-strov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R-delta boolean AND Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.

    Download full text (pdf)
    fulltext
  • 17.
    Nystedt, Patrik
    et al.
    Högskolan Väst, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Richter, Johan
    Mälardalens högskola, SWE.
    Simplicity of Ore monoid rings2019In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 530, p. 69-85Article in journal (Refereed)
    Abstract [en]

    Given a non-associative unital ring R, a monoid G and a set π of additive maps R→R, we introduce the Ore monoid ring R[π;G], and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D-structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids. © 2019 Elsevier Inc.

  • 18.
    Tarizadeh, Abolfazl
    et al.
    University of Maragheh, IRN.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Homogeneity in commutative graded ringsManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, we establish several new results on commutative G-graded rings where G is a totally ordered abelian group. McCoy’s theorem and Armendariz’ theorem are classical results in the theory of polynomial rings. We generalize both of these celebrated theorems to the more general setting of G-graded rings and simultaneously to the setting of ideals rather than to that of elements. Next, we give a complete characterization of invertible elements in G-graded rings. We generalize Bergman’s famous theorem (which asserts that the Jacobson radical of a Z-graded ring is a graded ideal) to the setting of G-graded rings and then proceed to give a natural and quite elementary proof of it. This generalization allows us to show that an abelian group is a totally ordered group if and only if the Jacobson radical of every ring graded by that group is a graded ideal, or equivalently, nonzero idempotents of every ring graded by that group are homogeneous of degree zero. Finally, some topological aspects of graded prime ideals are investigated.

  • 19.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Bimodules in Group Graded Rings2017In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, no 6, p. 1483-1494Article in journal (Refereed)
    Abstract [en]

    In this article we introduce the notion of a controlled group graded ring. Let G be a group, with identity element e, and let R = aS center dot (gaG) R (g) be a unital G-graded ring. We say that R is G-controlled if there is a one-to-one correspondence between subsets of the group G and (mutually non-isomorphic) R (e) -sub-bimodules of R, given by G aSc Ha dagger broken vertical bar aS center dot (haH) R (h) . For strongly G-graded rings, the property of being G-controlled is stronger than that of being simple. We provide necessary and sufficient conditions for a general G-graded ring to be G-controlled. We also give a characterization of strongly G-graded rings which are G-controlled. As an application of our main results we give a description of all intermediate subrings T with R (e) aS dagger T aS dagger R of a G-controlled strongly G-graded ring R. Our results generalize results for artinian skew group rings which were shown by Azumaya 70 years ago. In the special case of skew group rings we obtain an algebraic analogue of a recent result by Cameron and Smith on bimodules in crossed products of von Neumann algebras.

    Download full text (pdf)
    fulltext
  • 20.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Units, zero-divisors and idempotents in rings graded by torsion-free groups2024In: Journal of group theroy, ISSN 1433-5883, E-ISSN 1435-4446Article in journal (Refereed)
    Abstract [en]

    The three famous problems concerning units, zero-divisors and idempotents in group rings of torsion-free groups, commonly attributed to Kaplansky, have been around for more than 60 years and still remain open in characteristic zero. In this article, we introduce the corresponding problems in the considerably more general context of arbitrary rings graded by torsion-free groups. For natural reasons, we will restrict our attention to rings without non-trivial homogeneous zero-divisors with respect to the given grading. We provide a partial solution to the extended problems by solving them for rings graded by unique product groups. We also show that the extended problems exhibit the same (potential) hierarchy as the classical problems for group rings. Furthermore, a ring which is graded by an arbitrary torsion-free group is shown to be indecomposable, and to have no non-trivial central zero-divisor and no non-homogeneous central unit. We also present generalizations of the classical group ring conjectures.

    Download full text (pdf)
    fulltext
  • 21.
    Öinert, Johan
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Wagner, Stefan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Complex group rings and group C ∗ -algebras of group extensions2023In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 58, no 2, p. 387-397Article in journal (Refereed)
    Abstract [en]

    Let N and H be groups, and let G be an extension of H by N. In this article, we describe the structure of the complex group ring of G in terms of data associated with N and H. In particular, we present conditions on the building blocks N and H guaranteeing that G satisfies the zero-divisor and idempotent conjectures. Moreover, for central extensions involving amenable groups we present conditions on the building blocks guaranteeing that the Kadison–Kaplansky conjecture holds for the group C∗-algebra of G. © 2022, The Author(s).

    Download full text (pdf)
    fulltext
1 - 21 of 21
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf