Wala’a Alkasasbeh, Malik Bataineh, "Generalizations of S- Prime Ideals," WSEAS Transactions on Mathematics, vol. 20, pp. 694-699, 2021, DOI:10.37394/23206.2021.20.73
Wala’a Alkasasbeh, Malik Bataineh. Generalizations of S- Prime Ideals.
WSEAS Transactions on Mathematics. 2021;20:694-699. 10.37394/23206.2021.20.73
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.
Pages: 694-699 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 20, 2021, Art. #73 DOI: 10.37394/23206.2021.20.73
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