On reduced zero-divisor graphs of posets

2013/11/26 by Ashish Kumar Das, Das, Ashish Kumar, Deiborlang Nongsiang +1
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1311.6560

Abstract

In this paper we study some of the basic properties of a graph which is constructed from the equivalence classes of non-zero zero-divisors determined by 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.

Citations

• The Zero-Divisor Graph of a Commutative Ring
• Coloring of commutative rings
• On Beck’s coloring of posets

Related

• Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures
• A zero divisor graph determined by equivalence classes of zero divisors
• Zero-Divisor Graphs and Zero-Divisor Functors
• Genera of zero-divisor graphs with respect to ideals
• The Annihilating-Ideal Graph of Commutative Rings II