Theory of Algebraic Integers
Cambridge 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.
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algebraic integers algebraic number belong called class number coefﬁcients coeﬂicients complete complex integers congruence congruent modulo conjugate numbers consequently corresponding cyclotomic integers Dedekind deﬁne deﬁnition denote determinants Diophantus Dirichlet Disquisitiones Arithmeticae equivalent Euler evidently example exponent factors Fermat Fermat’s last theorem ﬁeld of ﬁnite ﬁeld Q ﬁg ﬁnd ﬁnding ﬁnite degree ﬁnite number ﬁnitely generated module ﬁrst form $2 Gauss Gaussian integers Gaussian prime greatest common divisor hence ideal numbers ideal theory incongruent modulo inﬁnite irrational numbers irreducible isomorphism Kummer Lagrange laws of divisibility least common multiple likewise nonzero number norm number 17 number divisible number of classes number theory numbers 01 ordinary integers polynomial prime ideal primitive root principal ideal proof Pythagorean triples quadratic character quadratic ﬁelds quadratic forms quadratic integers rational integers rational numbers rational prime relatively prime satisﬁes square mod theory of ideals theory of rational unique prime factorisation zero