AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS Elavarasan, Balasubramanian; Porselvi, Kasi;
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 subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by (P), and characterize its diameter.