A generalization of the smash product of a graded ring
type: Item
instance of: scholarly article
title: A generalization of the smash product of a graded ring
zbMATH Open document ID: 0653.16002
DOI: 10.1016/0022-4049(88)90093-X
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: It is proved here that the category of G-graded R-modules over a G-graded ring R (G is any group) is equivalent to the category of unital S-modules where \(S=R\#G\) * is a ring with local units (but without identity if G is infinite) defined analogously to the smash product of R with the dual of the group ring k[G] in the case of finite groups. Using this result a characterization of the graded Jacobson radical is obtained for infinite G.
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 4065190
zbMATH Keywords: category of G-graded R-modules
zbMATH Keywords: G-graded ring
zbMATH Keywords: category of unital S- modules
zbMATH Keywords: ring with local units
zbMATH Keywords: smash product
zbMATH Keywords: graded Jacobson radical
author: Margaret Beattie
reviewed by: L. Márki
MaRDI profile type: Publication
cites work: Morita equivalence for rings with local units
cites work: Morita equivalence for rings without identity
cites work: Group-Graded Rings, Smash Products, and Group Actions
cites work: Addendum to "Group-Graded Rings, Smash Products, and Group Actions"
cites work: Group graded rings
cites work: Q4339908
cites work: When is R-gr equivalent to the category of modules?
cites work: Q3957087
cites work: Group-Graded Rings and Duality
cites work: Q4198893
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description: scientific article; zbMATH DE number 4065190