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Injective modules and fp-injective modules over valuation rings

Francois Couchot
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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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Francois Couchot. 2004-09-27. Injective modules and fp-injective modules over valuation rings. https://doi.org/10.1016/s0021-8693(03)00373-9

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