Karagueuzian, Dikran B. and Symonds, Peter
(2007)
*The module structure of a group action on a polynomial ring: A finiteness theorem.*
Journal of the American Mathematical Society, 20 (4).
pp. 931-967.
ISSN 1088-6834

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Official URL: http://www.ams.org/jams/2007-20-04/S0894-0347-07-0...

## Abstract

Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries. For example, any indecomposable module that appears as a summand must also appear in low degree, and so the number of isomorphism types of such summands is finite. There are also applications to invariant theory, giving a priori bounds on the degrees of the generators.

Item Type: | Article |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 20 Nov 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/929 |

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