S-flat cotorsion pair

2024/03/14 by Bennis, Driss, Bouziri, Ayoub · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.09242

Abstract

Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we investigate the notion of S-cotorsion modules. An R-module C is called S-cotorsion if Ext¹_R(F,C) = 0 for every S-flat R-module F. Among other results, we establish that the pair (SF, SC), where SF denotes the class of all S-flat R-modules and SC denotes the class of all S-cotorsion modules, forms a hereditary perfect cotorsion pair. As applications, we provide characterizations of S-perfect rings in terms of S-cotorsion modules. We conclude the paper with results on SF-preenvelopes. Namely, we prove that if every module has an SF-preenvelope, then R is S-coherent. Furthermore, we establish the converse under the condition that R_S is a finitely presented R-module.

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• Cotorsion modules relative to a hereditary torsion theory

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