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 language | English |
---|---|
Pages (from-to) | 297-308 |
Number of pages | 12 |
Journal | Archiv der Mathematik |
Volume | 83 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2004 |