대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.45-58
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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NONNIL-S-COHERENT RINGS

  • Najib Mahdou (Department of Mathematics Faculty of Science and Technology of Fez, University S.M. Ben Abdellah Fez) ;
  • El Houssaine Oubouhou (Department of Mathematics Faculty of Science and Technology of Fez, University S.M. Ben Abdellah Fez)
  • 투고 : 2023.03.25
  • 심사 : 2023.04.13
  • 발행 : 2024.01.31
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초록

Let R be a commutative ring with identity. If the nilpotent radical N il(R) of R is a divided prime ideal, then R is called a ϕ-ring. Let R be a ϕ-ring and S be a multiplicative subset of R. In this paper, we introduce and study the class of nonnil-S-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are S-finitely presented. Also, we define the concept of ϕ-S-coherent rings. Among other results, we investigate the S-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-S-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.

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참고문헌

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