منابع مشابه
Group - Graded Rings and Duality
We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known results on skew group rings to corresponding results for large classes of group-graded rings. Finally we modify the construction slightly to handle infinite groups. Introduction. In the first section...
متن کاملStable Clifford Theory for Divisorially Graded Rings
Dade [D1, Theorem 7.4] obtained an important result on the equivalence of categories, extending the classical stable Clifford theory. He used the theory of strongly graded rings. Recently, this work has been generalized to arbitrary graded rings, see E. Dade [D2], [D3], J.L. Gómez Pardo and C. Nǎstǎsescu [GN ], C. Nǎstǎsescu and F. Van Oystaeyen [NVO2]. In the classical case the stable Clifford...
متن کاملCharacter Theory and Group Rings
While we were graduate students, Marty Isaacs and I worked together on the character theory of finite groups, studying in particular the character degrees of finite p-groups. Somewhat later, my interests turned to ring theory and infinite group theory. On the other hand, Marty continued with character theory and soon became a leader in the field. Indeed, he has had a superb career as a research...
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
متن کاملTight Closure of Finite Length Modules in Graded Rings
In this article, we look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does not depend upon dimension, the primary application is based on results known in dimension 2 due to the recent work of H. Brenner...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2000
ISSN: 0030-8730
DOI: 10.2140/pjm.2000.196.177