Overview
- This book was tranlated into French many years ago but never into English
- Hilbert's lucid writing style, bringing out the essentials of the subject is of particular interest now, at a time, when this subject has grown through several decades of intense research activity to one requiring a high degree of technical sophistication
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About this book
Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.
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Keywords
Table of contents (36 chapters)
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The Theory of General Number Fields
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Galois Number Fields
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Quadratic Number Fields
Bibliographic Information
Book Title: The Theory of Algebraic Number Fields
Authors: David Hilbert
DOI: https://doi.org/10.1007/978-3-662-03545-0
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1998
Hardcover ISBN: 978-3-540-62779-1Published: 20 August 1998
Softcover ISBN: 978-3-642-08306-8Published: 09 December 2010
eBook ISBN: 978-3-662-03545-0Published: 14 March 2013
Edition Number: 1
Number of Pages: XXXVI, 351