A GENERALIZED IDEAL BASED-ZERO DIVISOR GRAPHS OF NEAR-RINGS

- Journal title : Communications of the Korean Mathematical Society
- Volume 24, Issue 2, 2009, pp.161-169
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2009.24.2.161

Title & Authors

A GENERALIZED IDEAL BASED-ZERO DIVISOR GRAPHS OF NEAR-RINGS

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Abstract

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by . It is shown that if I is a completely reflexive ideal of N, then every two vertices in are connected by a path of length at most 3, and if contains a cycle, then the core K of is a union of triangles and rectangles. We have shown that if is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

Keywords

ideal-based zero-divisor graph;diameter;near-ring;ideal and cycle;

Language

English

Cited by

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