We seek to classify the sets of zero-divisors that form ideals based on their zero-divisor graphs. We offer full classification of these ideals within finite commutative rings with identity. We also provide various results concerning the realizability of a graph as a zero-divisor graph.
"Zero-divisor ideals and realizable zero-divisor graphs." Involve 2 (1) 17 - 27, 2009. https://doi.org/10.2140/involve.2009.2.17