| Classical Theory of Algebraic Numbers 2001 Edition Contributor(s): Ribenboim, Paulo (Author) |
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ISBN: 0387950702 ISBN-13: 9780387950709 Publisher: Springer OUR PRICE: $113.99 Product Type: Hardcover - Other Formats Published: March 2001 Annotation: One of the hallmarks of 19th century mathematics was the theory of algebraic numbers, developed by Gauss, Kummer and others. The theory is essential to the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptology. Ribenboim's aim is to give a clear self-contained exposition of this theory and to show how modern developments are rooted in the classical ideas. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Algebra - General |
| Dewey: 512.74 |
| LCCN: 00040044 |
| Series: Universitext |
| Physical Information: 1.44" H x 6.52" W x 9.44" (2.56 lbs) 682 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples. The introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields. Part one is devoted to residue classes and quadratic residues. In part two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals. part three is devoted to Kummer s theory of cyclotomic fields, and includes Bernoulli numbers and the proof of Fermat s Last Theorem for regular prime exponents. Finally, in part four, the emphasis is on analytical methods and it includes Dirichlet s Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas. A careful study of this book will provide a solid background to the learning of more recent topics, as suggested at the end of the book. |