Kurosch invariants for torsion-free modules over Nagata valuation domains

DOI10.1016/0022-4049(92)90120-5zbMath0781.13004OpenAlexW1964930762MaRDI QIDQ1208194

Paolo Zanardo

Publication date: 16 May 1993

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(92)90120-5

zbMATH Keywords

integral domaindirect decompositions of torsion-free modulesKurosch matrix invariantsNagata valuation domain

Mathematics Subject Classification ID

Integral domains (13G05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Valuation rings (13F30)

Related Items (11)

Definability of local abelian groups by their splitting rings ⋮ Modules over discrete valuation domains. III ⋮ Modules over discrete valuation domains. I ⋮ Indecomposable \(p\)-local torsion-free groups with quadratic and cubic splitting fields ⋮ Co-purely indecomposable modules over discrete valuation rings ⋮ Modules over domains large in a complete discrete valuation ring ⋮ Minimal modules over valuation domains ⋮ Valuation domains with a maximal immediate extension of finite rank ⋮ Indecomposable Modules Over Nagata Valuation Domains ⋮ Modules over discrete valuation domains. II ⋮ Commutative domains large in their \({\mathfrak M}\)-adic completions

Cites Work

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• Discrete valuation domains and ranks of their maximal extensions
• Polyserial modules over valuation domains
• On the analogue of Corner's finite rank theorem for modules over valuation domains
• Rank-two torsion-free modules over valuation domains
• On the completion of a valuation ring
• Decomposition Problems for Modules Over Valuation Domains
• Quasi-Direct Decompositions of Torsion-Free Abelian Groups of Infinite Rank.
• The Decomposability of Torsion Free Modules of Finite Rank
• A Duality for Torsion-Free Modules of Finite Rank Over a Discrete Valuation Ring
• Modules Over Dedekind Rings and Valuation Rings

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