Flat modules over valuation rings
| dc.creator | Couchot, Francois | |
| dc.date | 2007-06-01 | |
| dc.date.accessioned | 2026-07-07T08:03:51Z | |
| dc.date.available | 2026-07-07T08:03:51Z | |
| dc.description | Let $R$ be a valuation ring and let $Q$ be its total quotient ring. It is proved that any singly projective (respectively flat) module is finitely projective if and only if $Q$ is maximal (respectively artinian). It is shown that each singly projective module is a content module if and only if any non-unit of $R$ is a zero-divisor and that each singly projective module is locally projective if and only if $R$ is self injective. Moreover, $R$ is maximal if and only if each singly projective module is separable, if and only if any flat content module is locally projective. Necessary and sufficient conditions are given for a valuation ring with non-zero zero-divisors to be strongly coherent or $π$-coherent. A complete characterization of semihereditary commutative rings which are $π$-coherent is given. When $R$ is a commutative ring with a self FP-injective quotient ring $Q$, it is proved that each flat $R$-module is finitely projective if and only if $Q$ is perfect. | |
| dc.identifier | https://arxiv.org/abs/0706.0111 | |
| dc.identifier | http://arxiv.org/abs/0706.0111 | |
| dc.identifier | Journal of Pure and Applied Algebra 211 (10/2007) 235--247 | |
| dc.identifier | doi:10.1016/j.jpaa.2007.10.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129731 | |
| dc.subject | Rings and Algebras | |
| dc.subject | (Primary) 13F30, 13C11; (Secondary) 16D40 | |
| dc.title | Flat modules over valuation rings | |
| dc.type | text |