Some Issues About Formal Matrix Ring

In ring theory, different matrices have different functions. Which the formal matrix ring occupies a very important position.In the paper of Zhou Yijiang about a class of formal matrix rings,which introduces a number of properties in formal matrix ring Mn(R;s) that defined by a central element s in R.This article is inspired by this idea, extending some nature of the formal matrix ring through central element s and draw some relevant conclusions. This thesis consists of four chapters.The chapter one,we introduce some basic concepts and symbols,as well as the main background related to this article about the formal matrix ring Mn(R;s),and finally, make some promotion.The chapter two, we prove the existence and several useful properties of linear operator in the formal matrix ring Mn(R;s), this is get a good ready for the conclusion of the third chapter.The chapter three,on the basis of our second chapter,the multiplication has been portrayed in the formal matrix ring Mn(R;s), and we prove that the matrix multiplication depends on its track and orthogonality in the formal matrix ring Mn(R;s), Got an important conclusion of this article.The chapter four, We prove Bhattacharyya matrix theorem in the real still holds in formal matrix ring Mn{R;s).Bhattacharyya matrix theorem is that,every real (2n+1)×(2n+1) matrix can be written as a sum of a scalar,a skew matrix,and a matrix of rank≤n...