Abstract
The first important problem in the theory of number fields is the formulation of the laws concerning the factorisation of algebraic integers. These laws have a wonderful beauty and simplicity, exhibiting a precise analogy with the elementary laws of factorisation in the theory of rational integers and having the same fundamental importance. They were first discovered by Kummer for the special case of cyclotomic fields (Kummer (5,6)); their investigation for general number fields is due to Dedekind and Kronecker. The fundamental ideas of the theory are as follows.
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© 1998 Springer-Verlag Berlin Heidelberg
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Hilbert, D. (1998). Ideals of Number Fields. In: The Theory of Algebraic Number Fields. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03545-0_2
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DOI: https://doi.org/10.1007/978-3-662-03545-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08306-8
Online ISBN: 978-3-662-03545-0
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