On Reduced Zero-Divisor Graphs of Posets

Ashish Kumar Das; Deiborlang Nongsiang

doi:10.1155/2015/736326

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On Reduced Zero-Divisor Graphs of Posets

Ashish Kumar Das Deiborlang Nongsiang

Year: 2015 Journal: Journal of Discrete Mathematics Vol: 2015 Pages: 1-7 Publisher: Hindawi Publishing Corporation

DOI: 10.1155/2015/736326

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Abstract

We study some properties of a graph which is constructed from the equivalence classes of nonzero zero-divisors determined by the annihilator ideals of a poset. In particular, we demonstrate how this graph helps in identifying the annihilator prime ideals of a poset that satisfies the ascending chain condition for its proper annihilator ideals.

Keywords:

Annihilator Mathematics Partially ordered set Combinatorics Associated prime Zero divisor Graph Discrete mathematics Pure mathematics Prime (order theory) Algebra over a field

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Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Commutative Algebra and Its Applications

Physical Sciences → Mathematics → Algebra and Number Theory

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

On Reduced Zero-Divisor Graphs of Posets

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