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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)
  • 투고 : 2021.04.02
  • 심사 : 2021.07.23
  • 발행 : 2022.04.30

초록

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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참고문헌

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  2. H. Ahmed and H. Sana, Modules satisfying the S-Noetherian property and S-ACCR, Comm. Algebra 44 (2016), no. 5, 1941-1951. https://doi.org/10.1080/00927872.2015.1027377
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