Reference request on Associative Algebras

Question

I have to start studying associative algebras, with references to representation theory of associative algebras. Does anybody have some references? I'd like to have from very basic (advanced undergraduated) with examples to standard references in the field. Thank you!

Answer 1

For representation theory of associative algebras (and some more advanced topics) I recommend the book Introduction to representation theory by Etingof et al., which you can find online here.

Answer 2

Daniel Robert-Nicoud's answer gives a good reference. Allow me to list a few more:

• Associative Algebras, by Richard S. Pierce. Covers the structure of associative algebras, especially Artinian ones, and some representation theory.

• Representation Theory of Artin Algebras, by Maurice Auslander, Idun Reiten and Sverre O. Smalo. Covers representation theory, and especially Auslander-Reiten theory.

• Elements of the Representation Theory of Associative Algebras, by Ibrahim Assem, Daniel Simson and Andrzej Skowronski. Under the assumtion that the base ring is an algebraically closed field, this book covers representation theory of quivers and Auslander-Reiten theory, as well as some tilting theory.

• Bill Crawley-Boevey's lecture notes (pdf) on the representation theory of quivers.