The work in question has as its main objective to be an alternative material for the reader who seeks to start his studies in Homological Algebra. Here we will study the structures on sets called modules, an algebraic ...

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory ...

Given a finite-dimensional algebra it belongs to one of the following classes: derived tame or derived wild algebras. In this thesis our aim is to determine which finite dimensional K-algebras with three simple modules are ...

The Tame-Wild Dichotomy for derived categories establish that every finite dimensional algebra over an algebrically closed eld is either derived tame or derived wild ([7], [16]). We proved that a left serial algebra is ...