Triangular Matrix Algebra And Relative Homology

Let A be a finite dimension algebra over a field k and T2(A)=(?) be the triangular matrix algebra of algebra A, mod T2(A) denote the category of finitly generated T2(A) modules.This dissertation contains three parts. First, we introduce the definition of triangular matrix algebra. We investigate the representation type of T2(A), when A is a hereditary algebra of Dynkin type.Second, we investigate the indecomposable objects of T2(A). And cal-culate the Auslander Reiten translation of (M1,M.2,f) and the almost split sequence in mod T2(A). Further more,we prove that a partial tilting module of T2(A) has complement, when A is a hereditary algebra of Dynkin type.Last, we introduce some basic definitions of homological algebra. Let F be a perfect additive subfunctor of ExtA1(-,-). We prove that gl.dimF A<∞if p.dimF N<∞or i.dimF N<∞for every indecomposable A module N.