We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u + v = m, with m cube-free, all the terms beyond the first have a primitive divisor. 1. Statement of Main Theorem Let C denote a twist of the Fermat cubic, C : U + V 3 = mW 3 (1) with m a non-zero rational number. If K denotes any field of characteristic zero, the set C(K) of projective K-rational points satisfy...

In this article we discuss the graphs of the sets of zero-divisors of a ring. Now let R be a ring. Let G be a graph with elements of R as vertices such that two non-zero elements a, b ∈ R are adjacent if ab = ba = 0. We examine such a graph and try to find out when such a graph is planar and when is it complete etc. Mathematics Subject Classification: Primary 16-xx, 05-xx; Secondary 05C50

Let N be a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical I of N , denoted by ΓI(N). Further we obtain certain topological properties of Spec(N), the spectrum of 3-prime ideals of N and graph theoretic properties of ΓI(N). Using these properties, we discuss dominating sets and connected dominating sets of ΓI(N).

We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.

The aim of this article to follow the properties zero-divisor graph special idealization ring. We study wiener index zero-divisors some ring R(+)M and find clique number Γ(R(+)M) is ω (Γ(R(+)M)) = |M| − 1, where R an integral domain. also discuss when are Hamiltonian graph.