Algebraic Theory of Numbers. (AM-1), Volume 1 (Princeton Landmarks in Mathematics and Physics, 40)

In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to ^Ip^N-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition. "These are the authentic notes of a course on Theory of Numbers given in Princeton during the year 1938-1939. In view of the scarcity of books in English on theory of numbers, the author hopes that this outline of the fundamental arithmetic concepts and facts concerning algebraic fields will be of some use." -- Preface Let x be a field and k a subfield of x, so that x is a field "over k."