Theory of Algebraic Functions of One Variable

Language: English

Published by American Mathematical Society, US, 2012

0821883305 / 9780821883303

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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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Title
Theory of Algebraic Functions of One Variable
Author
Richard Dedekind, Heinrich Weber
Publisher
American Mathematical Society, US
Publication year
2012
Condition
New
Binding
Paperback
Language
English
ISBN 10
0821883305
ISBN 13
9780821883303
Item weight
295 grams
Dimensions
17.15 x 0.64 x 24.77 cm

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