Algebras of Linear Transformations

Douglas R. Farenick

This book is a linear-algebraic approach to the basic theory of finite-dimensional algebras, written for readers who have prior knowledge of undergraduate-level algebra. As such, the level of exposition is suitable for senior undergraduate and first-year graduate students. My aim is to present a balance of theory and example so that readers gain a firm understanding of the fundamental results, the motivating examples, and some of the important constructions. The study of finite-dimensional algebras provides a useful foundation for subsequent advanced work in a number of areas of mathematics, but the subject in itself is rich, elegant, and of classical importance.