Krull-Schmidt uniqueness fails dramatically over subrings of Z\(\oplus\dots \oplus Z\)

DOI10.1216/RMJ-1983-13-4-659zbMath0539.13005MaRDI QIDQ793789

Lawrence S. Levy

Publication date: 1983

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

cancellation of modulesdecomposition into indecomposable modulesKrull-Schmidt-Azumaya theorem

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Commutative rings and modules of finite generation or presentation; number of generators (13E15)

Related Items (12)

A Krull-Schmidt theorem for Noetherian modules ⋮ \({\mathbb{Z}}G_ n\)-modules, \(G_ n\) cyclic of square-free order n ⋮ Block rigid almost completely decomposable groups and lattices over multiple pullback rings ⋮ Unnamed Item ⋮ Wild torsion modules over Weyl algebras and general torsion modules over HNPs ⋮ Weak Krull-Schmidt for infinite direct sums of uniserial modules ⋮ Cancellation and direct summands in dimension 1 ⋮ The Extensional Structure of Commutative Noetherian Rings ⋮ Krull-Schmidt Fails for Artinian Modules ⋮ Dedekind-like behavior of rings with 2-generated ideals ⋮ Modules over Dedekind-like rings ⋮ Picard groups and torsion-free cancellation for orders in \(\mathbb Z \times \mathbb Z \times \mathbb Z\)

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