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arXiv · 1801.04820

$S$-almost perfect commutative rings

Silvana Bazzoni·Leonid Positselski
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Abstract

Given a multiplicative subset $S$ in a commutative ring $R$, we consider $S$-weakly cotorsion and $S$-strongly flat $R$-modules, and show that all $R$-modules have $S$-strongly flat covers if and only if all flat $R$-modules are $S$-strongly flat. These equivalent conditions hold if and only if the localization $R_S$ is a perfect ring and, for every element $s\in S$, the quotient ring $R/sR$ is a perfect ring, too. The multiplicative subset $S\subset R$ is allowed to contain zero-divisors.

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Silvana Bazzoni, Leonid Positselski. 2018-01-15. $S$-almost perfect commutative rings. https://doi.org/10.1016/j.jalgebra.2019.05.018

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