Related papers: Classical 2-absorbing submodules of modules over c…

All rings are commutative with $1\neq0$, and all modules are unital. The purpose of this paper is to investigate the concept of $2$-absorbing primary submodules generalizing $2$-absorbing primary ideals of rings. Let $M$ be an $R$-module. A…

In this paper, all rings are commutative with nonzero identity. Let M be an R-module. We introduce the concept of phi classical 1-absorbing prime submodules. A proper submodule N of M is a phi classical 1-absorbing prime submodule if…

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m \in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$…

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…

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…

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$…

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…

In this paper, we will introduce the concept of classical (resp. strongly classical) 2-absorbing second submodules of modules over a commutative ring as a generalization of 2-absorbing (resp. strongly 2-absorbing) second submodules 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 $N$ of $M$ is said to be a weakly classical 1-absorbing prime…

The aim of this article is to introduce the concept of graded $2$-absorbing coprimary submodules as a generalization of graded strongly $2$-absorbing second submodules, and explore some properties of this class. A non-zero graded…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded…

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 $e$, $R$ be a commutative $G$-graded ring with unity $1$ and $M$ be a $G$-graded unital $R$-module. In this article, we introduce the concept of graded $1$-absorbing prime submodule. A proper graded…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring, $M$ a graded $R$-module and $A\subseteq h(R)$ a multiplicatively closed subset of $R$. In this paper, we introduce the concept of graded $A$-2-absorbing…

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. In this paper, we introduce the notion of S-2-absorbing second submodules of M as a generalization of S-second submodules and…

In this paper, we will introduce the concept of 2-absorbing (resp. strongly 2-absorbing) secondary submodules of modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of these classes…

Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is…

Let $R$ be a graded commutative ring with non-zero unity $1$ and $M$ be a graded unitary $R$-module. In this article, we introduce the concepts of graded $\phi$-$2$-absorbing and graded $\phi$-$2$-absorbing primary submodules as…

Let $R_1$ and $R_2$ be commutative rings with $1\neq 0,\;M$ and $N$ be unitary $R_1-$module and $R_2-$module, respectively. $f:R_1\rightarrow R_2$ be a ring homomorphism and $\varphi: M\rightarrow N$ be an $R-$module homomorphism. This…

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible)…