WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
Generalizations of S- Prime Ideals
Authors: ,
Abstract: 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.