Which one to choose between Lang and Dummit Foote

Question

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

Answer 1

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.

Answer 2

I only used Dummit and Foote, so my answer should serve as a complement of Mr Hashi's.

First, I believe Dummit and Foote contains all the materials you need.

Second, the way I used this book is I took a year-long course on algebra, going through most of the important topics in D&F. My instructors assign important exercises in the book and I tried them all.

One caution about using this book is it contains too much material.Trying to read all of them at once would be a huge waste of time and well of frustration. You should choose on your own what you need and read the corresponding sections. After you go through most of the important sections, you can use this book as a reference. It is fantastic for this purpose.