Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On Weakly S-Primary Ideals of Commutative Rings

Version 1 : Received: 27 September 2021 / Approved: 29 September 2021 / Online: 29 September 2021 (10:31:20 CEST)

How to cite: Yetkin Celikeli, E.; Khashan, H. On Weakly S-Primary Ideals of Commutative Rings. Preprints 2021, 2021090486 (doi: 10.20944/preprints202109.0486.v1). Yetkin Celikeli, E.; Khashan, H. On Weakly S-Primary Ideals of Commutative Rings. Preprints 2021, 2021090486 (doi: 10.20944/preprints202109.0486.v1).

Abstract

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

Keywords

S--prime ideal; S-primary ideal; weakly S-prime ideal; S-n-ideal; weakly S-n-ideal; weakly S-primary ideal

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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