The Theory of Algebraic Numbers (Dover Books on Mathematics)

Pollard, Harry; Diamond, Harold G.

ISBN 10: 0486404544 / ISBN 13: 9780486404547

Published by Dover Publications, 2010

About this Item

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Bibliographic Details

• Title: The Theory of Algebraic Numbers (Dover Books on Mathematics)
• Publisher: Dover Publications
• Publication Date: 2010
• Language: English
• ISBN 10: 0486404544
• ISBN 13: 9780486404547
• Binding: Soft cover
• Condition: good

About this title

Synopsis

Detailed proofs and clear-cut explanations provide an excellent introduction to the elementary components of classical algebraic number theory in this concise, well-written volume.
The authors, a pair of noted mathematicians, start with a discussion of divisibility and proceed to examine Gaussian primes (their determination and role in Fermat's theorem); polynomials over a field (including the Eisenstein irreducibility criterion); algebraic number fields; bases (finite extensions, conjugates and discriminants, and the cyclotomic field); and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture (concluding with discussions of Pythagorean triples, units in cyclotomic fields, and Kummer's theorem).
In addition to a helpful list of symbols and an index, a set of carefully chosen problems appears at the end of each chapter to reinforce mathematics covered. Students and teachers of undergraduate mathematics courses will find this volume a first-rate introduction to algebraic number theory.