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)

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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.

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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