I am looking for a complete book on Abstract Algebra.By a "complete book" I mean to say a book that will cover all the topics of abstract algebra starting from group theory,ring theory ,field theory,Galois theory,Non-commutative rings ,jacobson radicals,Kummer ,cyclotomic extensions ,Krull topology and ending in Commutative algebra.
I searched on the web and found two only i.e
Dummit Foote and Lang's Algebra
I can't understand which book to start with.I have basic knowledge in group and ring theory and i also know some field theory.
Which one to buy between these two? I am confused.Please help
Best Answer
I only used Lang from those two, so I will tell you about that one.
Lang is not a book you learn from but a reference or a book to use for secondary literature. This information you can read anywhere(e.g. amazon) so I'll tell you my experience.
I bought Lang as a third year bachelor with the same knowledge as you approximately. The first year I browsed through it a few times and stared intimidating at me from my bookshelf. The exercises are too difficult and the text is too concise to help a starting mathematician grow.
After every algebra course I took, Commutative Algebra, Advanced Field Theory, Category theory, algebraic number theory etc. , I noticed my whole course was in that book and I could follow that chapter. Also you start liking the conciseness if you know more: you did not open that book for intuition building but to read how that one proof went.
I have never bought so much mathematics for 90 euro.