Stable isomorphism of modules over one-dimensional rings

DOI10.1016/0021-8693(87)90097-4zbMath0616.13006OpenAlexW2092084040MaRDI QIDQ1821148

Sylvia Wiegand, Roger Wiegand

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90097-4

zbMATH Keywords

group of units1-dimensional domainstable isomorphism classcancellation for stably isomorphic modules

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (17)

The genus of a module. II: Roiter's theorem, power cancellation and extension of scalars ⋮ Picard groups of singular affine curves over a perfect field ⋮ Direct sum behavior of lattices over sigma-I rings ⋮ Ranks of indecomposable modules over one-dimensional rings ⋮ Torsionfree modules over one-dimensional Noetherian rings ⋮ Direct-sum cancellation: Modules versus lattices¹ ⋮ Torsion in Tensor Products over One-Dimensional Domains ⋮ Finite representation type and direct-sum cancellation. ⋮ Cancellation and direct summands in dimension 1 ⋮ Curve singularities of finite Cohen-Macaulay type ⋮ Criteria for direct-sum cancellation, with an application to negative quadratic orders ⋮ Direct sum cancellation for modules over one-dimensional rings ⋮ PROJECTIVE PRESENTATIONS OF FINITELY GENERATED MODULES WITH LARGE ANNIHILATORS ⋮ FAILURE OF CANCELLATION FOR QUARTIC AND HIGHER-DEGREE ORDERS ⋮ Unique decompositions into ideals for noetherian domains. ⋮ Torsion-free modules over reduced Witt rings ⋮ Picard groups and torsion-free cancellation for orders in \(\mathbb Z \times \mathbb Z \times \mathbb Z\)

Cites Work

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• Cancellation over commutative rings of dimension one and two
• Power-cancellation of groups and modules
• Dedekind-like behavior of rings with 2-generated ideals
• The converse to a well known theorem on Noetherian rings
• On the structure of principal ideal rings

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