An ideal - based zero-divisor graph of posets
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The structure of a poset P with smallest element 0 is lookedat from two view points. Firstly, with respect to the Zariski topology, itis shown that Spec(P), the set of all prime semi-ideals of P, is a compactspace and Max(P), the set of all maximal semi-ideals of P, is a compactT1 subspace. Various other topological properties are derived. Secondly,we study the semi-ideal-based zero-divisor graph structure of poset P,denoted by GI (P), and characterize its diameter.
Abstract
The structure of a poset P with smallest element 0 is lookedat from two view points. Firstly, with respect to the Zariski topology, itis shown that Spec(P), the set of all prime semi-ideals of P, is a compactspace and Max(P), the set of all maximal semi-ideals of P, is a compactT1 subspace. Various other topological properties are derived. Secondly,we study the semi-ideal-based zero-divisor graph structure of poset P,denoted by GI (P), and characterize its diameter.
참고문헌 (10)
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