A good introductory book on Ring and Field theory with a view towards Number Theory ?

Question

Please suggest some good introductory books on Rings&Fields with a view towards Number Theory ?

Answer 1

The book of Ireland and Rosen is a very good introduction to the algebraic prerequisites in general, with emphasis on Euclidean rings, PIDs, UFDs, finite fields, and other things. Of course, it is mainly a book on number theory, and not on rings and fields.

Answer 2

While this book might be a bit advanced for the reader's purpose, Eisenbud's commutative algebra is excelent, although it may not be the best introduction. If you do look it up, you'll notice that it is 'with a view towards algebraic geometry,' which is very important in algebraic number theory.

Answer 3

This three books in my opinion are excellent to start:

-"A Brief Guide to Algebraic Number Theory" by H. P. F. Swinnerton-Dyer

-"Algebraic number theory" by Mollin R.A.

-"Problems in algebraic number theory" Ram Murty M., Esmonde J.