Rocky Mountain Journal of Mathematics

Zero-divisor graphs of modules via module homomorphisms

M. Afkhami, E. Estaji, K. Khashyarmanesh, and M.R. Khorsandi

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In this paper, using module endomorphisms, we extend the concept of the zero-divisor graph of a ring to a module over an arbitrary commutative ring. The main aim of this article is studying the interplay of module-theoretic properties of a module with graph properties of its zero-divisor graph.

Article information

Rocky Mountain J. Math., Volume 45, Number 1 (2015), 1-11.

First available in Project Euclid: 7 April 2015

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Zentralblatt MATH identifier

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 13C05: Structure, classification theorems

Zero-divisor graph endomorphism of a module girth decomposable module planar graph tensor product of graphs


Afkhami, M.; Estaji, E.; Khashyarmanesh, K.; Khorsandi, M.R. Zero-divisor graphs of modules via module homomorphisms. Rocky Mountain J. Math. 45 (2015), no. 1, 1--11. doi:10.1216/RMJ-2015-45-1-1.

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