Zero divisor graphs for modules over commutative rings
M Behboodi - Journal of Commutative Algebra, 2012 - JSTOR
Journal of Commutative Algebra, 2012•JSTOR
In this article, we give several generalizations of the concept of zero-divisor elements in a
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three
undirected (simple) graphs Γ*(𝑅𝑀)⊆ Γ (𝑅𝑀)⊆ Γ*(𝑅𝑀) which, for 𝑀= 𝑅, all coincide with the
zero-divisor graph of 𝑅. The main objective of this paper is to study the interplay of module-
theoretic properties of 𝑀 with graph-theoretic properties of these graphs.
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three
undirected (simple) graphs Γ*(𝑅𝑀)⊆ Γ (𝑅𝑀)⊆ Γ*(𝑅𝑀) which, for 𝑀= 𝑅, all coincide with the
zero-divisor graph of 𝑅. The main objective of this paper is to study the interplay of module-
theoretic properties of 𝑀 with graph-theoretic properties of these graphs.
Abstract
In this article, we give several generalizations of the concept of zero-divisor elements in a commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three undirected (simple) graphs Γ*(𝑅𝑀) ⊆ Γ(𝑅𝑀) ⊆ Γ*(𝑅𝑀) which, for 𝑀 = 𝑅, all coincide with the zero-divisor graph of 𝑅. The main objective of this paper is to study the interplay of module-theoretic properties of 𝑀 with graph-theoretic properties of these graphs.
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