Dummit and Foote on Galois and Representation Theory?

Question

At some point, I'd like to learn both Galois Theory and Representation Theory. I currently know a lot of Group Theory and Linear Algebra, as well as some Ring Theory. I was thinking of reading chapters 9, 13, and 14 in Dummit and Foote for Galois Theory, and Chapters 18 and 19 for Representation Theory.

Is Dummit and Foote a decent source for both of these topics? If so, do I need to read the chapters on Modules and Vector spaces to understand the representation theory chapters in particular (I know about vector spaces but not so much about modules)? And if not, are there any good recommendations for texts that are good introductions without being too dry?

Answer 1

The book "Galois Theory" of David Cox is a good introductory book.

If you want to learn representation theory of algebras, I recommend you to learn homological algebra first. A good book for learning homological algebra is "An introduction to homological algebra" of J. Rotman. There are two versions of this book, the second one is much more introductory. This book has a chapter about modules too. For representations of algebras you can read "Representation theory of assosiative algebras" of Assem, Simson and Skowronski (volume 1).

Answer 2

Dummit and Foote is great for an introduction to the two fields. Lots of examples and very readable. You certainly will not be an expert on either field after reading them. These suggestions by Marco Armenta are great for more advanced and thorough treatment of these vast areas. I think the modules section would be advisable to read if you want to understand representation theory at a more serious level.