On the compressed essential graph of a module over a commutative ring-Reference-Cited by-同舟云学术

On the compressed essential graph of a module over a commutative ring

Published:2020-10-16 Issue:07 Volume:14 Page:2150125
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Payrovi S. H.¹^ORCID,Babaei S.¹,Sengelen Sevim E.²

Affiliation:

1. Department of Mathematics, Imam Khomeini International University, P. O. Box: 34149-1-6818, Qazvin, Iran

2. Eski Silahtaraga Elektrik Santrali, Kazim Karabekir, Istanbul Bilgi University, Cad. No: 2/1334060, Eyup Istanbul, Turkey

Abstract

Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module. The compressed essential graph of [Formula: see text], denoted by [Formula: see text] is a simple undirected graph associated to [Formula: see text] whose vertices are classes of torsion elements of [Formula: see text] and two distinct classes [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is an essential ideal of [Formula: see text]. In this paper, we study diameter and girth of [Formula: see text] and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that [Formula: see text], whenever [Formula: see text] is Noetherian and [Formula: see text] is a finitely generated multiplication module with [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793557121501254

Reference15 articles.

1. The Set of Torsion Elements of a Module

2. The Zero-Divisor Graph of a Commutative Ring

3. On the Annihilator Submodules and the Annihilator Essential Graph

4. Coloring of commutative rings