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
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