## 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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