Let R be a commutative ring with identity. In this paper, we introduce the concept of 1-
absorbing prime ideals which is a generalization of prime ideals. A proper ideal I of R is …

The purpose of the paper is to introduce and study weakly 2-prime ideals in commutative
rings. Let A be a commutative ring with a nonzero identity. A proper ideal P of A is said to be …

Prime ideals and their generalizations are crucial in numerous research areas, particularly
in commutative algebra. The concept of generalization of prime ideals begins with the study …

Let R be a commutative ring with a nonzero identity. A proper ideal I of R is said to be a 1-
absorbing prime ideal if xyz∈ I for some nonunits x, y, z∈ R, then xy∈ I or z∈ I. It is well …

The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new
generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi …

Let R be a commutative ring with a nonzero identity. In this paper, we introduce the concept
of weakly 2-prime ideal which is a generalization of 2-prime ideal and both are …

In this paper, we describe some different variations of prime ideals in the context of rings of
continuous functions such as strongly prime ideals, almost prime ideals, n-absorbing ideals …

‎ Let $ R $ be a commutative ring with identity‎.‎ A proper ideal $ Q $‎‎ of $ R $ is called quasi
primary (weakly quasi primary) if whenever $ ab\in Q $($0\neq ab\in Q $) for some $ a, b\in …

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary
([4]) if for all nonunit a, b, c∈ R such that abc∈ I, then either ab∈ I or c∈ ${\sqrt {1}} $. The …

Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing
primary ideals which is a generalization of n-ideals and a subclass of 1-absorbing primary …