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Simplicity of Ore monoid rings
Högskolan Väst, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8095-0820
Mälardalens högskola, SWE.
2019 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 530, p. 69-85Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Academic Press Inc. , 2019. Vol. 530, p. 69-85
Keywords [en]
Differential monoid ring, Generalized monoid ring, Iterated Ore extension, Non-associative Ore extension, Ore monoid ring, Outer derivation, Simple ring
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-17864DOI: 10.1016/j.jalgebra.2019.04.003ISI: 000469166400003Scopus ID: 2-s2.0-85064169587OAI: oai:DiVA.org:bth-17864DiVA, id: diva2:1313012
Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-06-14Bibliographically approved

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Öinert, Johan

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