Archiv der Mathematik

, Volume 83, Issue 4, pp 297–308

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

  • M. C. R. Butler
  • J. M. Campbell
  • L. G. Kovács
Original Paper

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.

Mathematics Subject Classification (2000).

Primary 16G30 20C10 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  • M. C. R. Butler
    • 1
  • J. M. Campbell
    • 2
  • L. G. Kovács
    • 2
  1. 1.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUnited Kingdom
  2. 2.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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