Let R be a commutative ring with unity and let M be a left R-module. We define a proper
submodule N of M to be a weakly prime if whenever r &# 61646; R, x &# 61646; M, 0 &# …

In this paper, we extend the notion of 2-nil ideal introduced by Yetkin Celikel in [E. Yetkin
Celikel, 2-nil ideals of commutative rings, Bulletin of the Belgian Mathematical Society …

In this study, we aim to introduce the concept of a 1-absorbing prime submodule of an unital
module over a commutative ring with a non-zero identity. Let M be an R-module and N be a …

In this paper, we introduce the concept of graded weakly 2-absorbing primary submodules
as a generalization of graded weakly 2-absorbing primary ideals. A number of results …

Let R be a commutative ring with 1≠ 0 and I be a proper ideal of R. Then I is called a 2-
absorbing ideal of R if whenever abc∈ I for some a, b, c∈ R, then ab∈ I or bc∈ I or ac∈ I …

Let R be a commutative ring with identity. In this paper, we extend the concept of 1-
absorbing primary ideals to the concept of ֆ-1-absorbing primary ideals. Let ֆ: S (R)→ S …

SOME PROPERTIES OF 2-ABSORBING AND WEAKLY 2-ABSORBING PRIMARY IDEALS 1.
Introduction Throughout this paper all rings are commuta Page 1 Transactions on Algebra and …

In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital
module $ M $ over a commutative ring $ R $ having a nonzero identity. A proper submodule …

Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of
1-absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1 …

‎ Let $ R $ be a commutative ring with identity‎,‎ $ S $ a multiplicatively closed subset of $ R $‎,‎
and $ M $ be an $ R $-module‎.‎ The goal of this work is to introduce the notion of $ S $-pure …