• Title/Summary/Keyword: S-accr

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SOME RESULTS ON S-ACCR PAIRS

  • Hamed, Ahmed;Malek, Achraf
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.337-345
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    • 2022
  • Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B2) ⊆ (I : B3) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.