Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Weakly J-submodules of modules over commutative rings
View through CrossRef
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a unitary [Formula: see text]-module. By [Formula: see text] we denote the Jacobson radical of [Formula: see text]. The purpose of this paper is to introduce the concept of weakly [Formula: see text]-submodules generalizing [Formula: see text]-submodules. We call a proper submodule [Formula: see text] of [Formula: see text] a weakly [Formula: see text]-submodule if whenever [Formula: see text] for [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] Various properties and characterizations of weakly [Formula: see text]-submodules are investigated especially in the case of multiplication modules.
World Scientific Pub Co Pte Ltd
Title: Weakly J-submodules of modules over commutative rings
Description:
Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a unitary [Formula: see text]-module.
By [Formula: see text] we denote the Jacobson radical of [Formula: see text].
The purpose of this paper is to introduce the concept of weakly [Formula: see text]-submodules generalizing [Formula: see text]-submodules.
We call a proper submodule [Formula: see text] of [Formula: see text] a weakly [Formula: see text]-submodule if whenever [Formula: see text] for [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] Various properties and characterizations of weakly [Formula: see text]-submodules are investigated especially in the case of multiplication modules.
Related Results
Effects of cleaning in Saturn's rings
Effects of cleaning in Saturn's rings
Saturn's rings are well known for many good reasons, one of them being their brightness. Made of almost 99% water ice, they are by far the most ice-rich object of the solar system,...
WE-primary submodules and WE-quasi-prime submodules
WE-primary submodules and WE-quasi-prime submodules
In this paper we introduced and study two concepts one of is a subclass of a class of weakly primary submodules called WE-primary submodules and the other of a subclass of weakly ...
Weakly sdf-Absorbing Submodules Over Commutative Rings
Weakly sdf-Absorbing Submodules Over Commutative Rings
Let $R$ be a commutative ring with identity and $M$ a unital $R$-module. A proper submodule $N$ of $M$ is called a weakly square-difference factor absorbing submodule (briefly, wea...
(m, n)-Closed Submodules of Modules over Commutative Rings
(m, n)-Closed Submodules of Modules over Commutative Rings
Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈...
On Weakly S-Primary Ideals of Commutative Rings
On Weakly S-Primary Ideals of Commutative Rings
Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new ...
2-Visible Submodules and Fully 2-Visible Modules
2-Visible Submodules and Fully 2-Visible Modules
Let X be a T -module, T is a commutative ring with identity and K be a proper submodule of X. In this
paper we introduce the concepts of 2-visible submodules and fully 2-visible mo...
ATTACHED PRIMES UNDER SKEW POLYNOMIAL EXTENSIONS
ATTACHED PRIMES UNDER SKEW POLYNOMIAL EXTENSIONS
In the author's work [S. A. Annin, Attached primes over noncommutative rings, J. Pure Appl. Algebra212 (2008) 510–521], a theory of attached prime ideals in noncommutative rings wa...
WES-2-Absorbing Submodules and WEQ-2-Absorbing Submodules
WES-2-Absorbing Submodules and WEQ-2-Absorbing Submodules
In this research, we introduced and studied, the concepts of WES-2-absorbing submodules and WEQ-2-absorbing submodules as a stronger form of the concepts of weakly semi-2-absorbing...