Good book on field theory

It is Fields and Rings by Kaplansky!

it seems to be a small pamphlet but is concisely and very well composed. Only about 70 pages on Field Theory but almost all major results are there. What’s more, the exercises there are so good that I hav seen many people recommending them, including our Prof. Jacob who puts quite a few in his problem sets. The book is also what Prof. Jacob covered in his first eight week lectures.

I think the Ring Theory part, which is unusually put after Field Theory in the book, is also excellent lecture note. Anyway,  Kaplansky is a big guy in Algebra!

 

There may be other good books on Field Theory, such as Dummit’s and Rotman’s.

 

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