대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
  • /
  • Pages.237-250
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  • 2025
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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S-FLAT COTORSION PAIR

  • Driss Bennis (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat Rabat) ;
  • Ayoub Bouziri (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat Rabat)
  • 투고 : 2024.03.11
  • 심사 : 2024.08.29
  • 발행 : 2025.01.31
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초록

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 $Ext_{R}^{1}(F,C)=0$ 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 RS is a finitely presented R-module.

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참고문헌

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