Yetkin Celikel, E.; Khashan, H. A. On Weakly S-Primary Ideals of Commutative Rings. Journal of Algebra and Its Applications, 2023. https://doi.org/10.1142/s021949882450155x.
Yetkin Celikel, E.; Khashan, H. A. On Weakly S-Primary Ideals of Commutative Rings. Journal of Algebra and Its Applications, 2023. https://doi.org/10.1142/s021949882450155x.
Yetkin Celikel, E.; Khashan, H. A. On Weakly S-Primary Ideals of Commutative Rings. Journal of Algebra and Its Applications, 2023. https://doi.org/10.1142/s021949882450155x.
Yetkin Celikel, E.; Khashan, H. A. On Weakly S-Primary Ideals of Commutative Rings. Journal of Algebra and Its Applications, 2023. https://doi.org/10.1142/s021949882450155x.
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.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.