A zero divisor graph determined by equivalence classes of zero divisors

TL;DR

This paper explores how the zero divisor graph, constructed from equivalence classes of zero divisors in a commutative Noetherian ring, can reveal structural properties of the ring, including associated primes.

Contribution

It introduces a method to recover ring information, specifically associated primes, from the zero divisor graph based on equivalence classes.

Findings

Identifies associated primes from the zero divisor graph

Provides a way to recover ring structure from the graph

Establishes a correspondence between graph features and ring properties

Abstract

We study the zero divisor graph determined by equivalence classes of zero divisors of a commutative Noetherian ring R. We demonstrate how to recover information about R from this structure. In particular, we determine how to identify associated primes from the graph.