Zero-divisor graphs of nilpotent-free semigroups

Autor(en): Epstein, Neil
Nasehpour, Peyman
Stichwörter: ANNIHILATING-IDEAL GRAPH; Armendariz map; Comaximal graph; Graph invariants; Mathematics; Nilpotent-free semigroup; Zero-divisor graph
Erscheinungsdatum: 2013
Herausgeber: SPRINGER
Journal: JOURNAL OF ALGEBRAIC COMBINATORICS
Volumen: 37
Ausgabe: 3
Startseite: 523
Seitenende: 543
Zusammenfassung: 
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.
ISSN: 09259899
DOI: 10.1007/s10801-012-0377-x

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