Theory of algebraic integers

Includes index

0.1 General remarks ; 0.2 Squares ; 0.2.1 Pythagorean triples ; 0.2.2 Divisors and prime factorisation ; 0.2.3 Irrational numbers ; 0.2.4 Diophantus ; 0.3 Quadratic forms ; 0.3.1 Fermat. 0.3.2 The grit in the oyster 0.3.3 Reduction of forms ; 0.3.4 Lagrange's proof of the two squares theorem ; 0.3.5 Primitive roots and quadratic residues ; 0.3.6 Composition of forms ; 0.3.7 The class group ; 0.4 Quadratic integers ; 0.4.1 The need for generalised ""integers"" 0.4.2 Gaussian integers 0.4.3 Gaussian primes ; 0.4.4 Imaginary quadratic integers ; 0.4.5 The failure of unique prime factorisation ; 0.5 Roots of unity ; 0.5.1 Fermat's last theorem ; 0.5.2 The cyclotomic integers ; 0.5.3 Cyclotomic integers and quadratic integers. 0.5.4 Quadratic reciprocity 0.5.5 Other reciprocity laws ; 0.6 Algebraic integers ; 0.6.1 Definition ; 0.6.2 Basic properties ; 0.6.3 Class numbers ; 0.6.4 Ideal numbers and ideals ; 0.7 The reception of ideal theory ; 0.7.1 How the memoir came to be written. 0.7.2 Later development of ideal theory Acknowledgements ; Bibliography ; Part two: Theory of algebraic integers ; Introduction ; 1 Auxiliary theorems from the theory of modules ; 1. Modules and their divisibility ; 2. Congruences and classes of numbers

Dedekind memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in installments in French in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome.