Injective modules and fp-injective modules over valuation rings

2003/06/30 by F. Couchot, Francois Couchot
Mathematics · #Advanced Topology and Set Theory #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.RA

paper · pdf · doi:10.1016/s0021-8693(03)00373-9

published as Journal of Algebra 267 (2003) 359-376

openalex publication_date 2003/06/30 · arxiv created 2004/09/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is shown that each almost maximal valuation ring R such that every indecomposable injective module is countably generated, satisfies the following condition (C): each fp-injective module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring that sastisfies this condition (C) is almost maximal.

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