Related papers: On Weakly 1-Absorbing Prime Ideals

Let R be a commutative ring with $1\neq0$. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal. A proper ideal $I$ of $R$ is called a weakly 1-absorbing primary ideal if…

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

In this paper, we introduce $\phi$-1-absorbing prime ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity $1\neq0$ and $\phi:\mathcal{I}(R)\rightarrow\mathcal{I}(R)\cup\{\emptyset\}$ be a function where…

In this paper, we introduce the concepts of 1-absorbing prime and weakly 1-absorbing prime subsemimodules over commutative semirings. Let S be a commutative semiring with 1 \neq 0 and M an S-semimodule. A proper subsemimodule N of M is…

Let $G$ be a group with identity $e$ and $R$ be a $G$-graded commutative ring with nonzero unity $1$. In this article, we introduce the concept of graded strongly $1$-absorbing primary ideals. A proper graded ideal $P$ of $R$ is said to be…

Let $R$ be a commutative ring with nonzero identity. A. Yassine et al. defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of $1$-absorbing prime ideals as follows: a proper ideal $I$ of $R$ is said to be a…

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b \in R$ with $ab \in…

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 $N$ of $M$ is said to be a weakly classical 1-absorbing prime…

Let R be a commutative ring with identity. In this paper, we introduce the concept 1-absrbing primary ideal of R.

All rings are commutative with $1\neq0$. The purpose of this paper is to investigate the concept of weakly $n$-absorbing ideals generalizing weakly 2-absorbing ideals. We prove that over a $u$-ring $R$ the Anderson-Badawi's conjectures…

Let $R$ be a commutative ring with non-zero identity and $M$ be a unitary $R$-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule $N$ of $M$ is said to…

Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. Several properties of the hyperideals are provided. Moreover, we introduce the…

Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly $J$-ideals as a new generalization of $J$-ideals. We call a proper ideal $I$ of a ring $R$ a weakly $J$-ideal if whenever $a,b\in R$…

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several…

In this study, we aim to introduce the concept of classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $A$ with unity. A proper submodule $P$ of $M$ is said to be a classical 1-absorbing prime…

All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…

For the approx.ideal W of the approx.commutative ring R with unity in a descriptive relator space, after introducing the approx. prime ideal in [], this work demonstrates some special properties of the approx.ideals-specifically, the…

In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we…

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 proper submodule of M. For all non-unit elements a, b in R…

Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all graded ideals of $R$. Suppose that $\phi:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article, we introduce and…