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Diese Hardcover-Ausgabe ist Teil der TREDITION CLASSICS. Der Verlag
tredition aus Hamburg veroffentlicht in der Buchreihe TREDITION
CLASSICS Werke aus mehr als zwei Jahrtausenden. Diese waren zu
einem Grossteil vergriffen oder nur noch antiquarisch erhaltlich.
Mit TREDITION CLASSICS verfolgt tredition das Ziel, tausende
Klassiker der Weltliteratur verschiedener Sprachen wieder als
gedruckte Bucher zu verlegen - und das weltweit Die Buchreihe dient
zur Bewahrung der Literatur und Forderung der Kultur. Sie tragt so
dazu bei, dass viele tausend Werke nicht in Vergessenheit geraten
This book is the first English translation of the classic long
paper Theorie der algebraischen Functionen einer Veranderlichen
(Theory of algebraic functions of one variable), published by
Dedekind and Weber in 1882. The translation has been enriched by a
Translator's Introduction that provides historical background, and
extensive commentary embedded in the translation itself. The
translation, introduction, and commentary provide the first easy
access to this important paper for a wide mathematical audience:
students, historians of mathematics, and professional
mathematicians. Why is the Dedekind-Weber paper important? In the
1850s, Riemann initiated a revolution in algebraic geometry by
interpreting algebraic curves as surfaces covering the sphere. He
obtained deep and striking results in pure algebra by intuitive
arguments about surfaces and their topology. However, Riemann's
arguments were not rigorous, and they remained in limbo until 1882,
when Dedekind and Weber put them on a sound foundation. The key to
this breakthrough was to develop the theory of algebraic functions
in analogy with Dedekind's theory of algebraic numbers, where the
concept of ideal plays a central role. By introducing such concepts
into the theory of algebraic curves, Dedekind and Weber paved the
way for modern algebraic geometry.
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