Colloquium

Speaker: | Professor Hung-Jen Chiang-Hsieh (National Chung Cheng University) |

Title: | The Zero-divisor Graph of A Commutative Ring |

Time: | 2010-01-07 (Thu.) 15:00 - 16:00 |

Place: | Seminar Room 722, Institute of Mathematics (NTU Campus) |

Abstract: | Let R be a commutative ring with identity. The zero-divisor graph of R, denoted by !(R), is an undirected simple graph associated to the ring R such that its vertex set consists of all nonzero zero-divisors of R and that two distinct vertices are joined by an edge whenever the product of the vertices is zero. The interplay between the ring-theoretical properties and the graph-theoretical properties of the zero-divisor graph is the core of our study. In this talk, the basic properties of the zero-divisor graphs and their line graphs will be discussed. Moreover, I will introduce some genus formula for minimal embeddings of certain graphs into compact surfaces and apply them to classify rings with zero-divisor graphs of low genus. |

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