Weakly S-2-prime ideals of commutative rings
Sanem Yavuz\,^1, Bayram Ali Ersoy\,^2, Ünsal Tekir\,^3 and Ece Yetkin Çelikel\,^4
\,^{1,2}Department of Mathematics, Yildiz Technical University, Istanbul, Türkiye
\,^{3}Department of Mathematics, Marmara University, Istanbul, Türkiye
\,^{4}Department of Software Engineering, Hasan Kalyoncu University, Gaziantep, Türkiye
Pages 54-61 | Received 26 May 2024, Accepted 18 November 2024, Published 10 July 2025
Abstract
The objective of this paper is to introduce and investigate the concept of weakly S–2-prime ideals which are extensions of weakly 2-prime ideals in commutative rings. Let R be a commutative ring with identity and S be a multiplicative subset of R with 1\in S. A proper ideal Q of R with Q\cap S=\emptyset is called a weakly S–2-prime ideal of R if there exists an s\in S such that for all \alpha, \ \beta\in R with 0\neq\alpha\beta\in Q, we have s\alpha^{2}\in Q or s\beta^{2}\in Q. Various characterizations of weakly S–2-prime ideals are given and the relationship between weakly S–2-prime ideals and other classical ideals are illustrated by a diagram. For this relationship, a myriad of supporting examples and counter examples are presented. Moreover, this class of ideals is analyzed in idealization rings and amalgamated duplication along an ideal. Besides, the rings over which every weakly S–2-prime ideal is S–2-prime ideal is examined.
Keywords: 2-prime ideals, S–2-prime ideals, weakly 2-prime ideals, weakly S–2-prime ideals.
MSC numbers: Primary 13A15, 13C05; Secondary 13A99.
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