Journal of Algebra and Its Applications, ( ISI ), Volume (12), No (3), Year (2013-5) , Pages (12501731-12501739)

Title : ( On the cozero-divisor graphs and comaximal graphs of commutative rings )

Authors: Mojgan Afkhami , Kazem Khashyarmanesh ,

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Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ\\\'(R), is a graph with vertices in W^∗(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W^∗(R) are adjacent if and only if a not in bR and b not in aR. Also the comaximal graph is a graph with vertices all elements of R and two distinct vertices a and b are adjacent if and only if aR+bR = R. We denote the subgraph of the comaximal graph with vertex-set W∗(R), by Γ2(R). In this note, we study the relations between two graphs Γ\\\'(R) and Γ2(R). Also, we investigate the cozero-divisor graphs of idealizations of commutative rings.

Keywords

, Cozero, divisor graph; comaximal graph;
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@article{paperid:1040027,
author = {Mojgan Afkhami and Khashyarmanesh, Kazem},
title = {On the cozero-divisor graphs and comaximal graphs of commutative rings},
journal = {Journal of Algebra and Its Applications},
year = {2013},
volume = {12},
number = {3},
month = {May},
issn = {0219-4988},
pages = {12501731--12501739},
numpages = {8},
keywords = {Cozero-divisor graph; comaximal graph; idealization},
}

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%0 Journal Article
%T On the cozero-divisor graphs and comaximal graphs of commutative rings
%A Mojgan Afkhami
%A Khashyarmanesh, Kazem
%J Journal of Algebra and Its Applications
%@ 0219-4988
%D 2013

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