Valuation domains whose products of free modules are separable

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

It is proved that if $R$ is a valuation domain with maximal ideal $P$ and if $R_L$ is countably generated for each prime ideal $L$, then $R^R$ is separable if and only $R_J$ is maximal, where $J=\cap_{n\in\mathbb{N}}P^n$.

Mots clés: Valuation domain; torsion-free module; separable module

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. Valuation domains whose products of free modules are separable. Communications in Algebra, 2007, 35 (1), pp.2693--2697. ⟨hal-00176513⟩