Theory of Algebraic IntegersCambridge University Press, 1996/09/28 - 158 ページ The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877. This book is a translation of that work by John Stillwell, who adds a detailed introduction giving historical background and who outlines the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir offers a candid account of the development of an elegant theory and provides blow by blow comments regarding the many difficulties encountered en route. This book is a must for all number theorists. |
多く使われている語句
a₁ algebraic integers algebraic number B₁ belong called class number complete complex integers congruence congruent modulo consequently corresponding cyclotomic integers Dedekind definition denote determinants Diophantus Dirichlet Dirichlet's Vorlesungen Disquisitiones Arithmeticae equation equivalent Euler evidently example factors Fermat Fermat's last theorem field of finite finite degree finite number finitely generated module Gauss Gaussian integers Gaussian prime greatest common divisor hence ideal numbers incongruent modulo irrational numbers irreducible isomorphism Kummer Lagrange laws of divisibility least common multiple likewise mutually incongruent nonzero number norm number of classes number theory numbers a1 numbers ß ordinary integers polynomial prime ideal primitive root principal ideal proof quadratic fields quadratic forms quadratic integers rational coefficients rational integers rational numbers rational prime relatively prime square mod ẞn theory of ideals theory of rational unique prime factorisation Vorlesungen über Zahlentheorie w₁ x²+5y² zero