Representation Theory of Artin Algebras

Cambridge University Press, 1995 - 423 頁
This work is an introduction to the contemporary representation theory of Artin algebras, by three distinguished practitioners in the field. Beyond assuming some first-year undergraduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is suitable for any mathematicians (especially graduate students) wanting an introduction to this active field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However other foundational aspects of the subject are developed: for example, the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.

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