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Classical Theory of Algebraic Numbers

By: Paulo Ribenboim (Author)

Ksh 12,600.00
Format :

Format(s): DRM PDF

ISBN-13: 9780387216904

Publisher: Springer New York

Imprint: Springer

Publication Date: November 11th, 2013

Country of Publication: US

Language: English

Physical Edition EAN: 9780387950709

Category: Algebra , Number theory

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  • Description

  • Author Bio

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.

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