## 2007.184: The module structure of a group action on a polynomial ring: A finiteness theorem

2007.184:
Dikran B. Karagueuzian and Peter Symonds
(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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DOI: 10.1090/S0894-0347-07-00563-2

## 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 2000 > 16 Associative rings and algebras MSC 2000 > 20 Group theory and generalizations |

MIMS number: | 2007.184 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 20 November 2007 |

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