强P除环上方阵的酉相似理论(Ⅱ)

This is a continuation of the previous paper ( 1 ) . In this paper , a useful basic theorem that every selfconjugate matrix over the strong p division ring Ω is unitary similar to a tridiagorial matrix over the conter of Ω is given thus all of famous results involving selfconjugate matrices, positivedefinite selfcon jugate matrices, nonnegative selfconjugate matrix in the ordiniry com plex matrix theory are generalized to selfconjugate matrices over Ω . and Sigular decomuposition as well as polar decomposition in the ordinary complex matrix theory are also generalized to matrices over Ω .     

关于任意体上的一个矩阵方程组

In this peper,we give necessary and sufficient conditions for solvabilty of the system of matrix equations over an arbitrary skew field .The distinct expressions of the general solutions of the systerm are found and some properties of the soultons are also given.Thereupon the original projection matrix is generalized over an arbitrary skew field.     

强p除环上方阵的酉相似理论(Ⅰ)

Is this paper, the elementary reflexive marrix theory over the socalled strong p division risng Ω is given, by using this theory, many important matrix decompositions in the ordinary complex matrix theory (e.g., Schmidt decomposition, Cholesky decomposition, unitary equivalent decomposition,) are genera lized to matrices over Ω , and the theory that matrix unitary similar to Hessen berg matrix is established.     

THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS （AX- B, XC- D）

In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.     

Higher Level Orderings on Modules

The aim of this paper is to investigate higher level orderings on modules over commutative rings. On the basis of the theory of higher level orderings on fields and commutative rings, some results involving existence of higher level orderings are generalized to the category of modules over commutative rings. Moreover, a strict intersection theorem for higher level orderings on modules is established.     

Relative syzygies and grade of modules

Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω.     

REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES

In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the Urysohn-Nachbin lemma is presented which is quite different from the classical one.     

中心代数上一矩阵方程的中心对称与中心斜对称解

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.     

Generalized Inverses of Matrices over Rings

Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.     

A THEORETICAL APPROACH TO THERMAL PROPERTY OF ARRAY OF CYLINDERS EMBEDDED IN HOMOGENEOUS MATRIX

We investigate in this article the thermal conductivity of array of cylinders embedded in a homogeneous matrix. Using Green's function, we confirm that the method invented by Rayleigh can be generalized to deal with thermal property of these systems. A technique for calculating effective thermal conductivities of these systems is proposed. As an example, we consider a system with square symmetry, and a neat formula for effective thermal conductivity is derived. We show that the method also includes the proof of Keller theorem.