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.
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Descripción Mathematical Assoc Amer, 1968. Hard Cover. Estado de conservación: VG+ Near Fine 1968. Estado de la sobrecubierta: No DJ. 1st Ed, 3rd Pr 1968 #9. Nice clean cpy. Not a library book. No owner name. 143 pgs. Navy, gold title. 5X7.5. Nº de ref. de la librería 015905
Descripción John Wiley & Sons Inc, [Buffalo], 1950. hardcover. Estado de conservación: Good. Ships from the UK. Former Library book. Shows some signs of wear, and may have some markings on the inside. Nº de ref. de la librería GRP92253765