On Reduced Zero-Divisor Graphs of Posets

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.

Lattice automorphism and zero‐divisor graphs of lattices

“…In the past years, many authors have studied zero-divisor graphs of algebraic structures such as commutative rings, semigroups, partially ordered sets and lattices [1,3,5,10,12,13,14,16,17,18,19,24,25,28]. Apart from zero-divisor graphs, authors introduced and studied various graphs related to commutative rings, partially ordered sets and lattices.…”