Spectral properties of special matrices matrices have been widely applied. We focus on monomial matrices over a finite field Fp, p 6= 2. We describe a way to find the minimal annihilating polynomial, a set of linearly independent eigenvectors.

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules

Pairs (A,B) of mutually annihilating operators AB = BA = 0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1–58] by method of linear relations. The classification of (A,B) over any field was derived by Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636–654] from the classifi...

The purpose of this paper is to introduce new concepts in a module  over ring , the first one called e*- small essential submodule, which generalization second concept called e*-radical submodule radical and last e* - hollow module. We will prove some properties all these concepts.

In this paper we investigate decompositions of submodules in modules over a Proufer domain into intersections of quasi-primary and classical quasi-primary submodules. In particular, existence and uniqueness of quasi-primary decompositions in modules over a Proufer domain of finite character are proved. Proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decompo...

In this paper we study the following system of reaction-diffusion equations: ∂ /∂t = ∆ − V + λδ0, (0, x) ≡ 0, ∂V/∂t = − V, V (0, x) ≡ 1. Here (t, x) and V (t, x) are functions of time t ∈ [0,∞) and space x ∈ R. This system describes a continuum version of a model in which particles are injected at the origin at rate λ, perform independent simple symmetric random walks on Z, and are annihilated ...

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

The ππ and qq̄ annihilation mechanisms of dilepton production during relativistic nuclear collisions are studied. We focus on the modifications caused by the specific features of in-medium pion and quark states rather than by medium modification of the ρ-meson spectral density. The main ingredient emerging in our approach is a form-factor of the multi-pion (multi-quark) system. Replacing the usu...

Let $G$ be a group with identity $e$, $R$ commutative $G$-graded ring unity $1$ and $M$ unital $R$-module. In this article, we introduce the concept of graded $1$-absorbing prime submodule. A proper $R$-submodule $N$ is said to if for all non-unit homogeneous elements $x, y$ element $m$ $xym\in N$, either $xy\in (N :_{R} M)$ or $m\in N$. We show that new generalization submodules at same time i...

We study the space of functions on a finite-dimensional vector space over a field of odd order as a module for a symplectic group. We construct a basis of this module with the following special properties. Each submodule generated by a single basis element under the symplectic group action is spanned as a vector space by a subset of the basis and has a unique maximal submodule. From these prope...