Zero-divisor graphs of amalgamations

Salah Eddine Kabbaj; Abdeslam Mimouni

doi:10.7146/math.scand.a-105307

Zero-divisor graphs of amalgamations

Salah Eddine Kabbaj
, Abdeslam Mimouni^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let f : A → B be a homomorphism of commutative rings and let J be an ideal of B. The amalgamation of A with B along J with respect to f is the subring of A × B given by A^f J := {(a, f (a) + j) | a ∈ A, j ∈ J }. This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.

Original language	English
Pages (from-to)	174-190
Number of pages	17
Journal	Mathematica Scandinavica
Volume	123
Issue number	2
DOIs	https://doi.org/10.7146/math.scand.a-105307
State	Published - 5 Sep 2018

Bibliographical note

Publisher Copyright:
© 2018 Mathematica Scandinavica. All Rights Reserved.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.7146/math.scand.a-105307

Cite this

@article{a54cc0b12ca4484cbf9ade0acc15014f,

title = "Zero-divisor graphs of amalgamations",

abstract = "Let f : A → B be a homomorphism of commutative rings and let J be an ideal of B. The amalgamation of A with B along J with respect to f is the subring of A × B given by Af J := \{(a, f (a) + j) | a ∈ A, j ∈ J \}. This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.",

author = "Kabbaj, \{Salah Eddine\} and Abdeslam Mimouni",

year = "2018",

month = sep,

day = "5",

doi = "10.7146/math.scand.a-105307",

language = "English",

volume = "123",

pages = "174--190",

journal = "Mathematica Scandinavica",

issn = "0025-5521",

publisher = "Mathematica Scandinavica",

number = "2",

}

TY - JOUR

T1 - Zero-divisor graphs of amalgamations

AU - Kabbaj, Salah Eddine

AU - Mimouni, Abdeslam

PY - 2018/9/5

Y1 - 2018/9/5

N2 - Let f : A → B be a homomorphism of commutative rings and let J be an ideal of B. The amalgamation of A with B along J with respect to f is the subring of A × B given by Af J := {(a, f (a) + j) | a ∈ A, j ∈ J }. This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.

AB - Let f : A → B be a homomorphism of commutative rings and let J be an ideal of B. The amalgamation of A with B along J with respect to f is the subring of A × B given by Af J := {(a, f (a) + j) | a ∈ A, j ∈ J }. This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.

UR - https://www.scopus.com/pages/publications/85053180800

U2 - 10.7146/math.scand.a-105307

DO - 10.7146/math.scand.a-105307

M3 - Article

AN - SCOPUS:85053180800

SN - 0025-5521

VL - 123

SP - 174

EP - 190

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 2

ER -

Zero-divisor graphs of amalgamations

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this