On $S$-finite conductor rings

[摘要] Let $R$ be a commutative ring with nonzero identity and $S \subseteq R$ be a multiplicatively closed subset of $R$. In this paper, we introduce and study $S$-finite conductor rings. $R$ is said to be an $S$-finite conductor ring if $(0:a)$ and $Ra\cap Rb$ are $S$-finite ideals of $R$ for each $a,b\in R.$ Some basic properties of $S$-finite conductor rings are studied. For instance, we give necessary and sufficient conditions for a ring to be $S$-finite conductor. Also, we prove that every pre-Schreier $S$-finite conductor domain is an $S$-$GCD$ domain and the converse is true for some particular cases of $S$. Further, we examine the stability of these rings in localization and study the possible transfer to direct product, trivial ring extension and amalgamated algebra along an ideal.

[学科分类] 公共、环境与职业健康

[关键词] $S$-Finite conductor;Finite conductor;$S$-Coherence;$S$-Finite