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  Title

  Number fields

  Author

  Keune, Frans 1973- author (ISNI) 0000000369007545  

  Publisher:

  Radboud University Press,

  Pub date:

  [2023]

  Pages:

  1 online resource (XV, 569 pages) :

  ISBN:

  9789493296039

  Copy info:

  1 copy for Website.
  

  • 9789493296039
    
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  Number fields
  Keune, Frans 1973- author (ISNI) 0000000369007545
  

  Personal Author:

  Keune, Frans 1973- author (ISNI) 0000000369007545

  Title:

  Number fields / Frans Keune.

  Published/Produced:

  Nijmegen : Radboud University Press, [2023]

  Published/Produced:

  ©2023

  Physical descrip:

  1 online resource (XV, 569 pages) : illustrations

  Content Type:

  text

  Media Type:

  computer

  Carrier type:

  online resource

  Access restriction:

  Open access E-book: JSTOR Open Access collection

  Abstract:

  Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its main theorems are given using a 'classical' approach to class field theory, which is in a sense a natural continuation of the basic theory as presented in Part I. The classification is formulated in terms of generalized Dirichlet characters. This 'ideal-theoretic' version of class field theory dates from the first half of the twentieth century. In this book, it is described in modern mathematical language. Another approach, the 'idèlic version', uses topological algebra and group cohomology and originated halfway the last century. The last two chapters provide the connection to this more advanced idèlic version of class field theory. The book focuses on the abstract theory and contains many examples and exercises. For quadratic number fields algorithms are given for their class groups and, in the real case, for the fundamental unit. New concepts are introduced at the moment it makes a real difference to have them available.

  Issuing body:

  Made available online by JSTOR.

  Held by:

  WEBSITE

  Subject term:

  Algebraic number theory.

  Internet Access:

  https://www.jstor.org/stable/10.2307/jj.1666828