An ideal - based zero-divisor graph of posets
Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 79-85
Printed January 31, 2013
Balasubramanian Elavarasan and Kasi Porselvi
Karunya University, Karunya University
Abstract : The structure of a poset $P$ with smallest element $0$ is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that $Spec(P),$ the set of all prime semi-ideals of $P,$ is a compact space and $Max(P),$ the set of all maximal semi-ideals of $P,$ is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset $P, $ denoted by $G_I(P),$ and characterize its diameter.
Keywords : posets, semi-ideals, prime semi-ideals, zero-divisor graph
MSC numbers : 05C99, 06B35
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