Generalized S-prime ideals of commutative rings
Ahmed Hamed
Department of Mathematics, Faculty of Sciences, University of Monastir, Monastir, Tunisia
Pages 279–287 | Received 09 November 2023, Accepted 22 February 2024, Published 08 November 2024
Abstract
If 3 \leq n \leq \infty, Let R be a commutative ring with identity and S a multiplicative subset of R. The purpose of this paper is to introduce the concept of generalized S-prime ideals as a new generalization of prime ideals. An ideal P of R disjoint with S is called a generalized S-prime ideal if for all \alpha, \beta\in R there exists an s\in S such that \alpha\beta\in P implies s\alpha\in P or s\beta\in P. Several properties, characterizations and examples concerning generalized S-prime ideals are presented. We give a relationship between generalized S-prime ideals of a ring R and those of the idealization ring R(+)M. Also, we show that each ideal of R disjoint with S is contained in a minimal generalized S-prime ideal of R. This extends classical well-known result on minimal prime ideals.
Keywords: Generalized S-prime ideal, S-prime ideal.
MSC numbers: 13A15.
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