Challenging problems in algebra (book recommendation) Could you suggest me a book/web page where I can find challenging/hard problems in algebra (possibly with solutions) for an undergraduate student (groups, rings, fields, Galois theory)? Thanks in advance.
I already know Hernstein and Dummit books.
 A: As a fellow undergraduate, I'm working my way through the book Introduction to Abstract Algebra (4th Edition) by W. Keith Nicholson. The book contains all of the areas of Algebra you mentioned and more, and there are a plethora of problems for each of the sections on Group Theory, Ring Theory, Field Theory, Galois Theory, and so on. Each section has subsections with about 30 questions per subsection, so you're looking at about 500 to 600 questions in total I think. 
Albeit, the questions range from basic to difficult, but even if you're only interested in difficult problems, there are a bunch to do. 
The end of the book contains some of the solutions but you can get a corresponding solutions manual with the 4th edition that proves about half of the total questions.
The text book can be found here on Amazon.com: http://www.amazon.com/Introduction-Abstract-Algebra-Keith-Nicholson/dp/1118135350/ref=dp_ob_title_bkhttp://www.amazon.com/Introduction-Abstract-Algebra-Keith-Nicholson/dp/1118135350/ref=dp_ob_title_bk
