The Theory of Algebraic Numbers - (Dover Books on Mathematics) 3rd Edition by Harry Pollard & Harold G Diamond (Paperback)
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<p/><br></br><p><b> About the Book </b></p></br></br>Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.<p/><br></br><p><b> Book Synopsis </b></p></br></br>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.<br>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). <br>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.
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