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Simplicity of algebras via epsilon-strong systems
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
2020 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 162, no 2, p. 279-301Article in journal (Refereed) Published
Abstract [en]

We obtain sufficient criteria for simplicity of systems, that is, rings R that are equipped with a family of additive subgroups R-s for s is an element of S, where S is a semigroup satisfying R = Sigma (s is an element of S) R-s and RsRt subset of R-st for s, t is an element of S. These criteria are specialized to obtain sufficient criteria for simplicity of what we call s-unital epsilon-strong systems, that is, systems where S is an inverse semigroup, R is coherent, in the sense that R-s subset of R-t for all s, t is an element of S with s <= t and for each s is an element of S, the RsRs*-Rs*Rs -bimodule R-s is s-unital. As an application, we obtain generalizations of recent criteria for simplicity of skew inverse semigroup rings by Beuter, Goncalves, Oinert and Royer, and then for Steinberg algebras over non-commutative rings by Brown, Farthing, Sims, Steinberg, Clark and Edie-Michell.

Place, publisher, year, edition, pages
2020. Vol. 162, no 2, p. 279-301
Keywords [en]
graded ring; skew inverse semigroup ring; Steinberg algebra; partial action
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:hv:diva-15808DOI: 10.4064/cm7887-9-2019ISI: 000556329800008Scopus ID: 2-s2.0-85090404042OAI: oai:DiVA.org:hv-15808DiVA, id: diva2:1466883
Available from: 2020-09-14 Created: 2020-09-14 Last updated: 2020-10-07Bibliographically approved

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Nystedt, Patrik

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