Modules, algebras and quivers

Abstract

In this book, we assume that the reader has some familiarity with the classical theory of algebras and modules, category theory and homological algebra, such as can be gained from most textbooks in these areas. The first section of this chapter is devoted to recalling, mostly without proofs, some of the fundamental definitions and results from module theory needed later in the book. On the other hand, throughout this book, we shall continuously need to illustrate our results with examples. Therefore, in the second section, we give a concise introduction to the notion of quiver of an algebra, and explain how it can be used to compute examples. We also introduce two classes of algebras that are extensively used later on; namely, Nakayama algebras and hereditary algebras. In this second section, in contrast to the first, complete proofs are given.