Let G be a group with identity e and R be a G-graded commutative ring with 1 6= 0. In this
paper, we study the graded versions of 2-absorbing and weakly 2-absorbing ideals which …

Let R be a commutative ring with 1≠ 0. Recall that a proper ideal I of R is called a 2-
absorbing ideal of R if a, b, c∈ R and abc∈ I, then ab∈ I or ac∈ I or bc∈ I. A more general …

Let R be a commutative ring with identity. The notion of 2-absorbing ideal was introduced by
A. Badawi (Bull Aust Math Soc 75 (3): 417–429, 2007), as a generalization of prime ideal. A …

arXiv:1604.07656v1 [math.AC] 26 Apr 2016 Page 1 arXiv:1604.07656v1 [math.AC] 26 Apr 2016
ON (k, n)-CLOSED SUBMODULES ECE YETKIN CELIKEL Abstract. Let R be a commutative ring …

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 …

Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …

Most of the research on weakly prime and weakly 2-absorbing modules is for modules over
commutative rings. Only scatterd results about these notions with regard to non-commutative …

Let R be a commutative ring with identity and M be an unitary R-module. Let(M) bethe set
of all submodules of M, and:(M)(M){} be a function. We say that aproper …

Let R be a commutative ring with 1≠ 0. In his paper On 2-absorbing ideals of commutative
rings, Ayman Badawi introduces a generalization of prime ideals called 2-absorbing ideals …

Let R be a commutative ring with 1≠ 0. We introduce the concept of weakly 1-absorbing
primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is …