Communications of the Korean Mathematical Society (대한수학회논문집)

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SOME RESULTS ON S-ACCR PAIRS

  • Hamed, Ahmed (Department of Mathematics Faculty of Sciences) ;
  • Malek, Achraf (Department of Mathematics Faculty of Sciences)
  • Received : 2021.04.02
  • Accepted : 2021.07.23
  • Published : 2022.04.30
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Abstract

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.

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References

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