Structure theorems over polynomial rings |
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Authors: | Peter Symonds |
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Affiliation: | School of Mathematics, University of Manchester, PO Box 88, Manchester M60 1QD, UK |
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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]. |
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Keywords: | Polynomial ring Structure theorem Group action |
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