Abstract
Abstract In this paper, we introduce and study the notion of an đ-weakly prime ideal which is a generalization of a weakly prime ideal. Let đŽ be a commutative ring and đ a multiplicative set of đŽ. We define a proper ideal đ of đŽ to be đ-weakly prime if there exists s â S s\in S such that, for all a , b â A a,b\in A with 0 â a âą b â P 0\neq ab\in P , then s âą a â P sa\in P or s âą b â P sb\in P . We describe the behavior of an đ-weakly prime property across various ring-theoretic constructions such as direct product, homomorphic image, localization, trivial ring extensions and amalgamation rings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have