Injective modules and fp-injective modules over valuation rings

Details Injective modules and fp-injective modules over valuation rings Injective modules and fp-injective modules over valuation rings

2004-09-27

arxiv.org/abs/math/0409519v1

Journal of Algebra 267 (2003) 359-376

Mathematics

Rings and Algebras

Scientific paper

10.1016/S0021-8693(03)00373-9

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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