Valuation domains whose products of free modules are separable

Francois Couchot

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arXiv · 0710.0813

Valuation domains whose products of free modules are separable

Francois Couchot

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Abstract

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 $J=\cap_{n\in\mathbb{N}}P^n$.

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BibTeX RIS

Francois Couchot. 2007-10-03. Valuation domains whose products of free modules are separable. https://arxiv.org/abs/0710.0813

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