Structure theorems over polynomial rings
type: Item
instance of: scholarly article
title: Structure theorems over polynomial rings
zbMATH Open document ID: 1108.13007
author: Peter Symonds
published in: Advances in Mathematics
publication date: 2006-12-07T00:00:00Z
review text: Given a polynomial ring \(R\) over a field \(k\) and a finite group \(G\), let \(S\) be a finitely generated \(RG\)-module. A structure theorem for \(S\) is a set, indexed by subsets \(I\) of \(\{1,\dots,n\}\), of finitely generated \(kG\)-submodules \(X_I\) such that \(S\) is the direct sum of tensor products \(k[d_i:\,i\in I]\otimes_k X_I\). The author shows the equivalence of the existence of a structure theory for \(S\) and various other conditions, the most transparent being that only finitely many isomorphism classes of indecomposable \(kG\)-modules occur as summands of \(S\).
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 5078976
reviewed by: Phillip Schultz
MaRDI profile type: Publication
full work available at URL: j.aim.2006.02.012
OpenAlex ID: W2033503294
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DOI: 10.1016/J.AIM.2006.02.012
description: scientific article; zbMATH DE number 5078976