2023/03/24 by Ece Yetki̇n Çeli̇kel, Ece Yetkin Celikel, Hani A. Khashan · 6 citations
Mathematics · #Advanced Topics in Algebra #Combinatorics #Commutative Algebra and Its Applications #Ideal (ethics) #Local ring #Mathematics #Pure mathematics #Ring (chemistry) #Rings, Modules, and Algebras
paper · open access · doi:10.1142/s021949882450155x
published in Journal of Algebra and Its Applications 23(10) (World Scientific)
openalex publication_date 2023/03/24 · crossref created 2023/03/24 · crossref issued 2023/04/21 · crossref published 2023/04/21 · crossref published-online 2023/04/21 · crossref deposited 2024/08/06 · crossref published-print 2024/09/01 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a multiplicatively closed subset of [Formula: see text]. The purpose of this paper is to introduce the concept of weakly [Formula: see text]-primary ideals as a new generalization of weakly primary ideals. An ideal [Formula: see text] of [Formula: see text] disjoint with [Formula: see text] is called a weakly [Formula: see text]-primary ideal if there exists [Formula: see text] such that whenever [Formula: see text] for [Formula: see text], then [Formula: see text] or [Formula: see text]. The relationships among [Formula: see text]-prime, [Formula: see text]-primary, weakly [Formula: see text]-primary and [Formula: see text]-[Formula: see text]-ideals are investigated. For an element [Formula: see text] in any general ZPI-ring, the (weakly) [Formula: see text]-primary ideals are characterized where [Formula: see text]. Several properties, characterizations and examples concerning weakly [Formula: see text]-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 [Formula: see text]-decomposable ideals and [Formula: see text]-weakly Laskerian rings which are generalizations of [Formula: see text]-decomposable ideals and [Formula: see text]-Laskerian rings are introduced.