# AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS

• Published : 2009.11.30

#### Abstract

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

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#### Cited by

1. 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
2. On zero-divisors of near-rings of polynomials pp.1727-933X, 2018, https://doi.org/10.2989/16073606.2018.1455070