Open AccessGeneralizations of S- Prime Ideals
Author(s) -
Wala’a Alkasasbeh,
Malik Bataineh
Publication year - 2021
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2021.20.73
Subject(s) - ideal (ethics) , prime (order theory) , mathematics , associated prime , prime ideal , minimal ideal , generalization , prime element , commutative ring , multiplicative function , maximal ideal , primary ideal , ring (chemistry) , disjoint sets , combinatorics , boolean prime ideal theorem , discrete mathematics , radical of an ideal , identity (music) , semiprime ring , commutative property , principal ideal ring , law , physics , mathematical analysis , chemistry , organic chemistry , political science , acoustics
Let R be a commutative ring with identity and S be a multiplicative subset of R . In this paper we introduce the concept of almost S-prime ideal as a new generalization of S−prime ideal. Let P be a proper ideal of R disjoint with S. Then P is said to be almost S- prime ideal if there exists s ∈ S such that, for all x, y ∈ R if xy ∈ P − P 2 then sx ∈ P or sy ∈ P. Number of results concerning this concept and examples are given. Furthermore, we investigate an almost S- prime ideals of trivial ring extensions and amalgamation rings..