Abstract
Given a polynomial ring R over a field k and a finite group G, we consider a finitely generated graded RG-module S. We regard S as a kG-module and show that various conditions on S are equivalent, such as only containing finitely many isomorphism classes of indecomposable summands or satisfying a structure theorem in the sense of [D. Karagueuzian, P. Symonds, The module structure of a group action on a polynomial ring: A finiteness theorem, preprint, http://www.ma.umist.ac.uk/pas/preprints]. © 2006 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 408-421 |
Number of pages | 13 |
Journal | Advances in Mathematics |
Volume | 208 |
Issue number | 1 |
DOIs | |
Publication status | Published - 15 Jan 2007 |
Keywords
- Group action
- Polynomial ring
- Structure theorem