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http://dx.doi.org/10.4134/CKMS.c210112

SOME RESULTS ON S-ACCR PAIRS  

Hamed, Ahmed (Department of Mathematics Faculty of Sciences)
Malek, Achraf (Department of Mathematics Faculty of Sciences)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.2, 2022 , pp. 337-345 More about this Journal
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.
Keywords
S-accr; S-Noetherian; pair of rings;
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