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On S-weakly prime ideals of commutative rings by Najib Mahdou; Moutu Abdou Salam Moutui; Youssef Zahir is a Mathematics article available to read on EtoBox.

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## Abstract In this paper, we introduce and study the notion of an S-weakly prime ideal which is a generalization of a weakly prime ideal. Let A be a commutative ring and S a multiplicative set of A. We define a proper ideal P of A to be S-weakly prime if there exists s ∈ S s\in S such that, for all a , b ∈ A a,b\in A with 0 ≠ a ⁢ b ∈ P 0\neq ab\in P , then s ⁢ a ∈ P sa\in P or s ⁢ b ∈ P sb\in P . We describe the behavior of an S-weakly prime property across various ring-theoretic constructions such as direct product, homomorphic image, localization, trivial ring extensions and amalgamation rings.

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Author

Najib Mahdou; Moutu Abdou Salam Moutui; Youssef Zahir

Publisher

Walter de Gruyter GmbH

Published

2022

Language

EN

Field

Mathematics (Physical Sciences)