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Ideals of Number Fields

In: The Theory of Algebraic Number Fields

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  • David Hilbert

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.

Suggested Citation

  • David Hilbert, 1998. "Ideals of Number Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 2, pages 9-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03545-0_2
    DOI: 10.1007/978-3-662-03545-0_2
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