The Theory of Algebraic Numbers (Dover Books on Mathematics)

About this book

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 Fermats 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 Kummers 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.