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).

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding blocks of the group algebra. Mathematics Subject Classification (2000): 19A22 20C20

In this paper, for an odd prime p, the differential spectrum of the power function x pk+1 2 in Fpn is calculated. For an odd prime p such that p ≡ 3 mod 4 and odd n with k|n, the differential spectrum of the power function x pn+1 pk+1 + p n −1 2 in Fpn is also derived. From their differential spectrums, the differential uniformities of these two power functions are determined. We also find some...

In this paper a bijection between the set of prime ideals of a Leavitt path algebra L K (E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x −1 ] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra L K (E) is primitive are also found.

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations, population dynamics, etc. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed ...

Let S0 (p) denote the sphere spectrum localized at an odd prime p. Then we have the first beta element β1 ∈ π2p2−2p−2(S (p)), whose cofiber we denote by W . We also consider a generalized Smith-Toda spectrum Vr characterized by BP∗(Vr) = BP∗/(p, vr 1). In this note, we show that an element of π∗(Vr ∧W ) gives rise to a beta element of homotopy groups of spheres. As an application, we show the e...

Based on a study of basic properties of cyclic graphs of prime order, we give an algorithm for computing lower bounds of classical Ramsey numbers. Our algorithm reduces certain amount of computation of cyclic graphs of prime order, since only some of them normalized cyclic graphs require computation in our method. Using the algorithm, we construct ten cyclic graphs of prime order to obtain new ...

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...

Previous research has shown that stimuli rendered invisible through masking can be sufficiently processed to induce nonconscious influences and facilitate subsequent recognition. However, masking paradigms are methodologically restricted such that stimuli cannot be presented for longer than a few tens of milliseconds, potentially restricting the strength of nonconscious influences. By adapting ...

Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...