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S-coherent property in trivial extension and in amalgamated duplication

Salah Eddine Mahdou|Mohamed Chhiti
대한수학회 (The Korean Mathematical Society)|2023.07|대한수학회논문집 (Communications of the KMS)|제38권 제3호|pp. 705-714|DOI 10.4134/CKMS.c220260

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참고문헌

키워드

trivial ring extension$S$-coherence$S$-finitely presented$S$-finiteamalgamation algebra along an ideal
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초록

Bennis and El Hajoui have defined a (commutative unital) ring $R$ to be $S$-coherent if each finitely generated ideal of $R$ is a $S$-finitely presented $R$-module. Any coherent ring is an $S$-coherent ring. Several examples of $S$-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the $S$-coherent property to trivial ring extensions and amalgamated duplications.

Abstract

Bennis and El Hajoui have defined a (commutative unital) ring $R$ to be $S$-coherent if each finitely generated ideal of $R$ is a $S$-finitely presented $R$-module. Any coherent ring is an $S$-coherent ring. Several examples of $S$-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the $S$-coherent property to trivial ring extensions and amalgamated duplications.

참고문헌 (18)

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관련 논문AI추천

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