Theory of algebraic integers

the long version

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 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. The memoir gives a candid account of Dedekind's development of an elegant theory as well as providing blow by blow comments as he wrestles with the many difficulties encountered en-route.