Woodcock, C.F. (2007) A commutative analogue of the group ring. Journal of Pure and Applied Algebra, 210 (1). pp. 193-199. ISSN 0022-4049.
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| 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. In the case when G is an elementary Abelian p-group it turns out that R-G is closely related to the symmetric algebra over F-p of the dual of G. We intend in subsequent papers to explore the close relationship between G and R-G in the case of a general (possibly non-Abelian) group G. 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 |
|---|---|
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |
| Depositing User: | Chris F Woodcock |
| Date Deposited: | 04 Jun 2008 16:39 |
| Last Modified: | 14 Jan 2010 14:11 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/3170 (The current URI for this page, for reference purposes) |
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