3 papers
math.RA2024
S-J-Ideals: A Study in Commutative and Noncommutative Rings
Alaa Abouhalaka, Hatice Çay, Bayram Ali Ersoy
In this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that ma…
math.RA2024
S-Prime Right Submodules and an S-Version of Prime Avoidance
Alaa Abouhalaka
Let S be an m-system of a ring R, and P a submodule of a right R-module M. This paper, presents the notion of S-prime submodule and provides some properties and equivalent definiti…
math.RA2022
Almost prime ideals in noncommutative rings
Alaa Abouhalaka, Sehmus Findik
A proper ideal of a commutative ring with identity is an almost prime ideal if implies or . In this paper we define almost prime ide…