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 S-Accr Pairs Commun. Korean Math. Soc.Published online November 22, 2021 Ahmed Hamed and achraf malek Faculty of Sciences of Monastir; Faculty of Sciences of Monastir Abstract : Let R included in T be an extension of commutative rings and $S$ a multiplicative subset of R. 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 $(I:B)\subseteq (I:B^2)\subseteq (I:B^3)\subseteq\cdots$ 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 $R\subseteq A\subseteq T$ satisfies $S$-accr. Using this concept, we give an $S$-version of several different known results. Keywords : S-accr, S-Noetherian, Pair of rings MSC numbers : 13B; 13C; 13E05; 13E10 Full-Text :

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