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Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8445-3936
Abstract [en]

Let $G$ be a group and let $S=\bigoplus_{g \in G} S_g$ be a $G$-graded ring. Given a normal subgroup $N$ of $G$, there is a naturally induced $G/N$-grading of $S$. It is well-known that if $S$ is strongly $G$-graded, then the induced $G/N$-grading is strong for any $N$. The class of epsilon-strongly graded rings was recently introduced by Nystedt, Ã–inert and Pinedo as a generalization of unital strongly graded rings. We give an example of an epsilon-strongly graded partial skew group ring such that the induced quotient group grading is not epsilon-strong. Moreover, we give necessary and sufficient conditions for the induced $G/N$-grading of an epsilon-strongly $G$-graded ring to be epsilon-strong. Our method involves relating different types of rings equipped with local units (s-unital rings, rings with sets of local units, rings with enough idempotents) with generalized epsilon-strongly graded rings.

Keywords [en]
group graded ring, epsilon-strongly graded ring, Leavitt path algebra, partial skew group ring.
National Category
Algebra and Logic
Identifiers
OAI: oai:DiVA.org:bth-17806DiVA, id: diva2:1304127
Funder
The Crafoord Foundation, 20170843Available from: 2019-04-11 Created: 2019-04-11 Last updated: 2019-04-24Bibliographically approved
In thesis
1. The structure of epsilon-strongly graded rings with applications to Leavitt path algebras and Cuntz-Pimsner rings
Open this publication in new window or tab >>The structure of epsilon-strongly graded rings with applications to Leavitt path algebras and Cuntz-Pimsner rings
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The research field of graded ring theory is a rich area of mathematics with many connections to e.g. the field of operator algebras. In the last 15 years, algebraists and operator algebraists have defined algebraic analogues of important operator algebras. Some of those analogues are rings that come equipped with a group grading. We want to reach a better understanding of the graded structure of those analogue rings. Among group graded rings, the strongly graded rings stand out as being especially well-behaved. The development of the general theory of strongly graded rings was initiated by Dade in the 1980s and since then numerous structural results have been established for strongly graded rings.

Place, publisher, year, edition, pages
Karlskrona: Blekinge Tekniska Högskola, 2019
Series
Blekinge Institute of Technology Licentiate Dissertation Series, ISSN 1650-2140 ; 7
Keywords
group graded ring, epsilon-strongly graded ring, chain conditions, Leavitt path algebra, partial crossed product, Cuntz-Pimsner rings
National Category
Algebra and Logic
Identifiers
urn:nbn:se:bth-17809 (URN)978-91-7295-376-5 (ISBN)
Presentation
2019-05-15, G340, Valhallavägen 1, Karlskrona, 14:35 (English)
Funder
The Crafoord Foundation, 20170843 Available from: 2019-04-11 Created: 2019-04-11 Last updated: 2019-06-11Bibliographically approved

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Lännström, Daniel

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