# AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

• Elavarasan, Balasubramanian ;
• Porselvi, Kasi
• Published : 2013.01.31
• 36 6

#### 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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#### Cited by

1. Normal subgroup based power graphs of a finite group vol.45, pp.8, 2017, https://doi.org/10.1080/00927872.2016.1236122
2. Poset Properties Determined by the Ideal - Based Zero-divisor Graph vol.54, pp.2, 2014, https://doi.org/10.5666/KMJ.2014.54.2.197