ABSTRACT

This chapter considers the notions of finite quivers and their representations and give the main results of this theory. It discusses some main notions and results of the representation theory of finite dimensional algebras. The chapter discovers that quivers with finite and nonempty sets Q 0 and Q 1. It discusses with an introduction to valued graphs which can be considered as some generalizations of ordinary graphs. The chapter also considers the concepts of species which were first introduced by p. Gabriel and their connection with valued graphs and valued quivers. A dimension category is said to be of strongly unbounded type if it possesses the following properties: The well known Brauer-Thrall conjecture states that any K-algebra is either of finite type or strongly unbounded type.