Number Fields [Paperback]

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, down-to-earth manner. It thus avoids local methods, for example, and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.1: A Special Case of Fermats Conjecture.- 2: Number Fields and Number Rings.- 3: Prime Decomposition in Number Rings.- 4: Galois Theory Applied to Prime Decomposition.- 5: The Ideal Class Group and the Unit Group.- 6: The Distribution of Ideals in a Number Ring.- 7: The Dedekind Zeta Function and the Class Number Formula.- 8: The Distribution of Primes and an Introduction to Class Field Theory.- Appendix A: Commutative Rings and Ideals.- Appendix B: Galois Theory for Subfields of C.- Appendix C: Finite Fields and Rings.- Appendix D: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.

It is well structured and gives the reader lots of motivation to learn more about the subject. It is one of the rare books which can help students to learn new stuff by themselves by solving the numerous exercises which cover very deep and important results & . The prerequisites for the reader are kept to a minimum making this book accessible to students at a much earlier stage than usual textbooks on algebraic number theory.

A book unabashedly devoted to number fields is a fabulous idea. & it goes without saying that the exercises in the book  and there are many  are of glƒ$