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On reduced zero-divisor graphs of posets. (English) Zbl 1334.05058

Summary: 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.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
06A07 Combinatorics of partially ordered sets
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