What is the absolute best abstract algebra book for graduate students? I was wanting a book that covers algebra in the most comprehensive manner possible, at about the level of Hungerford's Algebra. I was wondering if Carstensen's Abstract Algebra in the Sigma Series in Pure Mathematics is a good text. Any recommendations?
Hi ForMyThunder! Which kind of algebra are you interested in? There are a lot of branches out there! I've always found "Commutative algebra with a view on algebraic geometry" by Eisenbud wonderful. But that focusses on commutative algebra. Another great book is the algebra books by Bourbaki, but Bourbaki's style is often criticized...
"Absolute best" is subjective, but if you're looking for a comprehensive book, check out Lang. http://www.amazon.com/Algebra-Serge-Lang/dp/038795385X Harder than Hungerford, but definitely a good book to have on your shelf.
the modern standards are artin, dummit and foote, hungerford, lang. a little older but excellent are: jacobson, van der waerden, and sah. i have free algebra notes on my web page for math courses 843-4-5, and 8000[6]. see my profile for address. many other people have possibly better and certainly nicer looking ones on their sites. james milne's site is a treasure trove of wonderfully well written and excellent books and notes.
Has anyone read this book? http://www.amazon.com/Abstract-Alge...008X/ref=sr_1_1?ie=UTF8&qid=1308192770&sr=8-1 If so, how was it?