What Are the Best Advanced Textbooks for Studying Abstract Algebra?

[thequirk]

My current algebra class is using Fraleigh's "First Course in Abstract Algebra", and it doesn't feel very challenging (and is extremely verbose!). I'd like to study the subject deeper, since I really enjoy it. I picked up Lang's "Undergraduate Algebra", which seems to be much better, but if there is something better, I would really love to hear about it.

 

[morphism]

I like Herstein's Topics in Algebra. It has great problems, and Herstein's writing is very lucid.

Others on this forum like to recommend Artin's Algebra. There have been many threads about this: do a search!

 

[charng]

As a fellow enthusiast of abstract algebra, I can understand your desire for a more challenging and concise text. While Fraleigh's "First Course in Abstract Algebra" may be a standard text in many algebra courses, it is important to remember that different texts cater to different learning styles and levels of difficulty. Lang's "Undergraduate Algebra" is certainly a step up in terms of rigor and depth, but there are also other options out there that may suit your needs.

One text that I would recommend is Dummit and Foote's "Abstract Algebra". This text is known for its clear and concise presentation of abstract algebra concepts, as well as its challenging exercises. It covers a wide range of topics, including group theory, ring theory, and field theory, making it a comprehensive resource for studying abstract algebra at a deeper level.

Another option is Artin's "Algebra". This text is known for its intuitive and geometric approach to abstract algebra, making it a great choice for students who prefer a more visual and conceptual understanding of the subject. It also covers a variety of topics, including group theory, ring theory, and Galois theory, and has challenging exercises to reinforce learning.

Ultimately, the best text for you will depend on your individual learning style and preferences. I would recommend exploring different texts and seeing which one resonates with you the most. Additionally, supplementing your studies with additional resources, such as online lectures or problem sets, can also enhance your understanding of abstract algebra and make your learning experience more challenging and enjoyable.