AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

Title & Authors
AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS
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 $\small{T_1}$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $\small{G_I}$ (P), and characterize its diameter.
Keywords
posets;semi-ideals;prime semi-ideals;zero-divisor graph;
Language
English
Cited by
1.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.197-201
1.
Normal subgroup based power graphs of a finite group, Communications in Algebra, 2017, 45, 8, 3251
2.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph, Kyungpook mathematical journal, 2014, 54, 2, 197
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