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ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING

T. TAMIZH CHELVAM

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, India

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and

S. NITHYA

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, India

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https://doi.org/10.1142/S1793830913500079Cited by:5 (Source: Crossref)

Abstract

In this paper, we associate the graph Γ_I(N) to an ideal I of a near-ring N. We exhibit some properties and structure of Γ_I(N). For a commutative ring R, Beck conjectured that both chromatic number and clique number of the zero-divisor graph Γ(R) of R are equal. We prove that Beck's conjecture is true for Γ_I(N). Moreover, we characterize all right permutable near-rings N for which the graph Γ_I(N) is finitely colorable.

Keywords:

AMSC: 16Y30, 68R10

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