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

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- by Dikran B. Karagueuzian and Peter Symonds
- J. Amer. Math. Soc.
**20**(2007), 931-967 - DOI: https://doi.org/10.1090/S0894-0347-07-00563-2
- Published electronically: April 11, 2007
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## 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.## References

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## Bibliographic Information

**Dikran B. Karagueuzian**- Affiliation: Mathematics Department, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000
- Email: dikran@math.binghamton.edu
**Peter Symonds**- Affiliation: School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom
- Email: Peter.Symonds@manchester.ac.uk
- Received by editor(s): March 17, 2005
- Published electronically: April 11, 2007
- © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**20**(2007), 931-967 - MSC (2000): Primary 16W22; Secondary 20C20
- DOI: https://doi.org/10.1090/S0894-0347-07-00563-2
- MathSciNet review: 2328711