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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

On zs-ideals of commutative rings

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pp. 2273–2287Vol. 27Issue 8December 2024DOI: 10.47974/JDMSC-1846 Crossmark XML
Received:
08 Mar 2023
Published Online:
18 Dec 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1846
Pages:
2273–2287

Abstract

Let R be a commutative ring with nonzero unity and S a multiplicatively closed subset (m.c.s) of R. An S-disjoint ideal of R is called zS-ideal if there exists s = sI ϵ S and whenever MS(a) ⸦ MS(b) for some a ϵ I and b ϵ R, then sb ϵ I, where MS(a) = {MaxS(R) : sa ϵ M for some s ϵ S}, for each a ϵ R. In the present paper, we introduce and study the concept of zS-ideal which is an extension of the notion of the z-ideals. We generalize some well-known results on z-ideal to zS-ideal. In addition, many examples, characterizations, and properties of zS-ideal are given. We also investigate the relation between z-ideals and zS-ideals of a commutative ring.

Keywords

Commutative ringz-idealszs-idealsS-primeS-maximal ideals

Subject Classifications

13A1513B3013B10

References

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