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

M. C.R. Butler*, J. M. Campbell, L. G. Kovács

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)

    Abstract

    Let ∧ = ℤG be the integer group ring of a group, G, of prime order. A main result of this note is that every ∧-module with a free underlying abelian group decomposes into a direct sum of copies of the well-known indecomposable ∧-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 ∧-lattices.

    Original languageEnglish
    Pages (from-to)297-308
    Number of pages12
    JournalArchiv der Mathematik
    Volume83
    Issue number4
    DOIs
    Publication statusPublished - Oct 2004

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