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

Abstract.

Let $\Lambda = \mathbb{Z}G$ 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.