Geodesic
Zero-divisor graphs of nilpotent-free semigroups
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 523-543.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an Armendariz map between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs.
Keywords: zero-divisor graph, Armendariz map, graph invariants, annihilating-ideal graph, comaximal graph, nilpotent-free semigroup 
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     title = {Zero-divisor graphs of nilpotent-free semigroups},
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Epstein, Neil; Nasehpour, Peyman. Zero-divisor graphs of nilpotent-free semigroups. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 523-543. http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a2/