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The Theory of Algebraic Numbers (Dover Books on Mathema 1.4tics) - Softcover
Book 108 of 302: Dover Books on Mathematics
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.
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.
"synopsis" may belong to another edition of this title.
Synopsis
A brief introduction for undergraduate students and teachers, presenting detailed proofs and explanations of the elementary components of classical algebraic number theory. Begins with divisibility and Gaussian primes, and proceeds to ideal classes and class numbers and the Fermat conjecture. A slightly revised and totally unexpurgated edition of t
"About this title" may belong to another edition of this title.
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The Theory of Algebraic Numbers (Dover Books on Mathematics)
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Dover Publications (edition Subsequent), 2010
ISBN 10: 0486404544
ISBN 13: 9780486404547
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The Theory of Algebraic Numbers (Dover Books on Mathematics)
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The Theory of Algebraic Numbers (Dover Books on Mathematics)
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Dover Publications Inc., 1998
ISBN 10: 0486404544
ISBN 13: 9780486404547
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