2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139238It 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 $J=\cap_{n\in\mathbb{N}}P^n$.Rings and Algebras13C10, 13F99, 13G05text