A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors

By Sandra Spiroff, Cameron Wickham. 2007

110 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6e1573d4b237d738c68258176a170317eba0b21c

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

On Zero Divisor Graphs (2012, background): “R// D .”
On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n (2021, background): “This graph was first defined in [17] and their properties for Zpn were investigated in [13].”
Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph (2012, background): “As in [24], ΓE(R)will denote the (undirected) graph whose vertices are the elements of RE\{[0]R, [1]R} such that distinct vertices [r]R and [s]R are adjacent if and only if [r]R[s]R = [0]R, if and only if rs = 0.”