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Simplicity of algebras via epsilon-strong systems
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.ORCID-id: 0000-0001-6594-7041
2020 (engelsk)Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 162, nr 2, s. 279-301Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2020. Vol. 162, nr 2, s. 279-301
Emneord [en]
graded ring; skew inverse semigroup ring; Steinberg algebra; partial action
HSV kategori
Identifikatorer
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
Tilgjengelig fra: 2020-09-14 Laget: 2020-09-14 Sist oppdatert: 2020-10-07bibliografisk kontrollert

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