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Group graded rings
Miriam Cohen,Louis Rowen +1 more
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The notion of strongly G-graded rings was introduced by Dade as discussed by the authors, who showed that R × R → 1 is a group graded ring if and only if R1 is a crossed product R1 * G.Abstract:
Let R be a group graded ring . The map ( , ): R × R →1 defined by: (x,y) = (xy)1 , is an inner product on R. In this paper we investigate aspects of nondegeneracy of the product, which is a generalization of the notion of strongly G —graded rings,introduced by Dade. We show that various chain conditions are satisfied by R if and only if they are satisfied by R1 , and that when R1 is simple artinian, then R is a crossed product R1 * G. We give conditions for simple R-modules to be completely reducible R1 -modules . Finally, we prove an incomparability theorem,when G is finite abelian.read more
Citations
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Group-graded rings, smash products, and group actions
Miriam Cohen,Susan Montgomery +1 more
Journal ArticleDOI
Group Gradings on Associative Algebras
TL;DR: In this article, the authors give a description of all G-gradings on R, provided that G is an abelian group and R is Artinian semisimple.
Journal ArticleDOI
Skew group algebras in the representation theory of artin algebras
Idun Reiten,Christine Riedtmann +1 more
TL;DR: In this article, the authors considered the case where the values of y lie in the center Z(A) of /i. In this paper we assume that y is the trivial map of /1G instead of/i * G, and the elements as C,,,c li gi.
Book
Graded Rings and Graded Grothendieck Groups
TL;DR: The first systematic account of the graded Grothendieck group, a powerful invariant in algebra which has recently been adopted to classify the Leavitt path algebras, can be found in this paper.
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Hopf algebra actions
Miriam Cohen,Davida Fishman +1 more
TL;DR: In this article, a Maschke-type theorem for group-graded rings is proved for Hopf algebras H acting on H-module algeses A # H-modules.
References
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Journal ArticleDOI
Group-graded rings and modules
TL;DR: In this paper, the authors consider the representation of a group H related to a normal subgroup N of H by a group ring fH of H, over any coefficient ring f, as graded by the factor group G = H/N.
Book
Graded and Filtered Rings and Modules
TL;DR: Graded and filtered rings and modules as discussed by the authors were used to construct ring and module structures for the first time in the early nineties and have been used extensively in the last decade.
Journal ArticleDOI
Prime ideals in crossed products of finite groups
Martin Lorenz,D. S. Passman +1 more
TL;DR: In this article, the relationship between the prime ideals of a finite group of automorphisms and the prime ranks of the fixed ring of a fixed automorphism over the ring is discussed.