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 instalments 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.
Dedekind's memoir gives a candid account of his development of an
elegant theory as well as providing blow-by-blow comments as he
wrestled with the many difficulties encountered en route. A must
for all number theorists.
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