AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

- Journal title : Communications of the Korean Mathematical Society
- Volume 28, Issue 1, 2013, pp.79-85
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2013.28.1.079

Title & Authors

AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

Elavarasan, Balasubramanian; Porselvi, Kasi;

Elavarasan, Balasubramanian; Porselvi, Kasi;

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 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.

Keywords

posets;semi-ideals;prime semi-ideals;zero-divisor graph;

Language

English

Cited by

References

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