Semisimple rings graded by inverse semigroups
type: Item
instance of: scholarly article
title: Semisimple rings graded by inverse semigroups
zbMATH Open document ID: 0910.16024
published in: Journal of Algebra
publication date: 1999-04-15T00:00:00Z
review text: Let \(S\) be an inverse semigroup, and let \(R=\bigoplus_{s\in S}R_s\) be a faithful \(S\)-graded ring. If all group-graded subrings \(R_G=\bigoplus_{s\in G}R_s\) are semiprimitive (semiprime) for all maximal subgroups \(G\) of \(S\), then \(R\) is semiprimitive (semiprime). If all group-graded subrings \(R_G\) have no nonzero nil (locally nilpotent) ideals for all maximal subgroups \(G\) of \(S\), then \(R\) has no nonzero nil (locally nilpotent) ideals; a similar result holds when each such \(R_G\) has no nonzero nil right ideals.
reviewed by: Mark L. Teply
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 1214127
zbMATH Keywords: semiprime rings
zbMATH Keywords: inverse semigroups
zbMATH Keywords: group-graded rings
zbMATH Keywords: semiprimitive rings
zbMATH Keywords: maximal subgroups
author: A. V. Kelarev
MaRDI profile type: Publication
full work available at URL: jabr.1997.7391
OpenAlex ID: W2034786246
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DOI: 10.1006/JABR.1997.7391
description: scientific article; zbMATH DE number 1214127