Injective modules and fp-injective modules over valuation rings

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. Injective modules and fp-injective modules over valuation rings. Journal of Algebra, 2003, 267, pp.359-376. ⟨10.1016/S0021-8693(03)00373-9⟩. ⟨hal-00002951⟩