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http://dx.doi.org/10.4134/CKMS.2013.28.1.079

AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS  

Elavarasan, Balasubramanian (Department of Mathematics School of Science and Humanities Karunya University)
Porselvi, Kasi (Department of Mathematics School of Science and Humanities Karunya University)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.1, 2013 , pp. 79-85 More about this Journal
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;
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