Valuation domains with a maximal immediate extension of finite rank

DOI10.1016/j.jalgebra.2009.08.023zbMath1189.13017arXiv0901.1651OpenAlexW2074290469MaRDI QIDQ2268595

Francois Couchot

Publication date: 8 March 2010

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

Full work available at URL: https://arxiv.org/abs/0901.1651

zbMATH Keywords

torsion-free modulevaluation domainmaximal immediate extensiontotal defect

Mathematics Subject Classification ID

Valuation rings (13F30) Other special types of modules and ideals in commutative rings (13C13) Completion of commutative rings (13B35)

Related Items (3)

Indecomposable injective modules of finite Malcev rank over local commutative rings ⋮ Definable coaisles over rings of weak global dimension at most one ⋮ Archimedean domains of skew generalized power series

Cites Work

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• Discrete valuation domains and ranks of their maximal extensions
• Kurosch invariants for torsion-free modules over Nagata valuation domains
• Splitting fields for torsion-free modules over discrete valuation rings. I
• On strongly flat modules over integral domains
• Flat modules over valuation rings
• The minimal splitting field for a finite rank torsion free module over an almost maximal valuation domain
• Decomposition Problems for Modules Over Valuation Domains
• Indecomposable Modules Over Nagata Valuation Domains
• LOCAL RINGS OF BOUNDED MODULE TYPE ARE ALMOST MAXIMAL VALUATION RINGS
• Linearly Compact Modules and Rings

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