On The Filtration Dimension Of The Morita Context

This thesis primarily consists of two parts. In the first part, we mainly give the forms of the simple modules in Mod (Γ),when Morita Context satis-fies some conditions,and discuss the relation between global dimensions of Γ and of A; In the second part,we mainly discuss the relation between the finitistic filtration di-mensions of Γ and A when Morita Context where A is a standardly stratified algebra.Morita Context is introduced by Morita, Morita Context rings is an importan-t class of noncommutative rings. Many researchers are interested in their properties. Triangular matrix ring is just the special case of Morita Context rings. In the first part of this thesis,we give the forms of the simple modules in Mod(Γ) are (S,0,0,0) and (0, U,0,0),where S and U are simple∧-modules, when Morita Context satisfies some conditions.Furthermore,we construct the composition sequence of the Morita Context,and then proved gl.dimΓ≤gl.dimA. In the second part of this pa-per,we study the properties of the Morita Context on standardly stratification. Through constructing the filtration on Morita Context rings, we proved the relation between fini-tistic filtration dimensions of Γ and of A,where and A is standardly stratified algebra,that is, fin.dimF(Δ)<2fin.dimF(Δ)(∧).