Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On Weakly 1-Absorbing Primary Ideals of Commutative Rings
View through CrossRef
Let [Formula: see text] be a commutative ring with [Formula: see text]. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal [Formula: see text] of [Formula: see text] is said to be weakly 1-absorbing primary if whenever nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text]. A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals. Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
Title: On Weakly 1-Absorbing Primary Ideals of Commutative Rings
Description:
Let [Formula: see text] be a commutative ring with [Formula: see text].
We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal.
A proper ideal [Formula: see text] of [Formula: see text] is said to be weakly 1-absorbing primary if whenever nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text].
A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals.
Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
Related Results
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 ...
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,...
Weakly 2‐Absorbing Ideals in Almost Distributive Lattices
Weakly 2‐Absorbing Ideals in Almost Distributive Lattices
The concepts of weakly 2‐absorbing ideal and weakly 1‐absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1‐abso...
S-Ideals: A Unified Framework for Ideal Structures via Multiplicatively Closed Subsets
S-Ideals: A Unified Framework for Ideal Structures via Multiplicatively Closed Subsets
In this paper, we study ideals defined with respect to arbitrary multiplicatively closed subsets S⊆R of a commutative ring R. An ideal I⊆R is called an S-ideal if for all a,b∈R, th...
Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings
Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings
Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a...
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...
On 2-nil Primary Ideals of Commutative Rings
On 2-nil Primary Ideals of Commutative Rings
The present article addresses the concept of 2-nil primary ideals in commutative rings, expanding the comprehension of ideal categories such as 2-nil, 2-absorbing and quasi primar...
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...