Formal Triangular Matrix Rings And Modules Over Rings Of Morita Contexts

In this paper, we discuss the properties of formal triangular matrix rings from two different angles.The paper consists of two chapters. In chapter 1, we characterize various ring theoretic properties of formal triangular matrix rings. Some results are obtained on these rings concerning properties such as being respectively PS, CESS, reduced, Baer, von Neumann regular, strong regular or weak regular. In chapter 2, we discuss the properties of modules over rings of Morita contexts that is a extension of formal triangular matrix rings. Firstly, we describe submodules and quotient modules of these modules. Secondly, we discuss two essential properties of submodules of these modules and then use these to characterize two kinds of modules over rings of Morita contexts. Lastly, we think about the construction of maximal(resp. simple) submodules of these modules.