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A commutative analogue of the group ring

Woodcock, Chris F. (2007) A commutative analogue of the group ring. Journal of Pure and Applied Algebra, 210 (1). pp. 193-199. ISSN 0022-4049. (doi:10.1016/j.jpaa.2006.09.011) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:3170)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.jpaa.2006.09.011

Abstract

Throughout, all rings R will be commutative with identity element. In this paper we introduce, for each finite group G, a commutative graded Z-algebra R-G. This classifies the G-invariant commutative R-algebra multiplications on the group algebra R[G] which are cocycles (in fact coboundaries) with respect to the standard "direct sum" multiplication and have the same identity element.

Here we show that the Krull dimension of R-G is the maximal rank r of an elementary Abelian subgroup E of G unless either E is cyclic or for some such E its normalizer in G contains a non-trivial cyclic group which acts faithfully on E via "scalar multiplication" in which case it is r + 1.

Item Type: Article
DOI/Identification number: 10.1016/j.jpaa.2006.09.011
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Christopher Woodcock
Date Deposited: 04 Jun 2008 16:39 UTC
Last Modified: 06 Feb 2020 04:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/3170 (The current URI for this page, for reference purposes)
Woodcock, Chris F.: https://orcid.org/0000-0003-4713-0040
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