CMA Research Report

MRR03-008

On infinite rank integral representations of groups and orders of finite lattice type

Abstract:  Let Λ = ZG be the integer group ring of a group, G, of prime order. A main result of this note is that every Λ-module with a free underlying abelian group decomposes into a direct sum of copies of the well-known indecomposable Λ-lattices of finite rank. The first part of the proof reduces the problem to one about countably generated modules, and works in a wider context of suitably restricted modules over orders of finite lattice type of a quite general type. However, for countably generated modules, use is seemingly needed of the classical theory of Λ-lattices.

AMS Classification:  20C10
Date:  23 September 2003

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