A Classical Invitation to Algebraic Numbers and Class Fields
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A Classical Invitation to Algebraic Numbers and Class Fields: (Universitext)

A Classical Invitation to Algebraic Numbers and Class Fields: (Universitext)


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From the reviews/Aus den Besprechungen: "...Fur den an der Geschichte der Zahlentheorie interessierten Mathematikhistoriker ist das Buch mindestens in zweierlei Hinsicht lesenswert. Zum einen enthalt der Text eine ganze Reihe von historischen Hinweisen, zum anderen legt der Autor sehr grossen Wert auf eine moglichst allseitige Motivierung seiner Darlegungen und versucht dazu, insbesondere den wichtigen historischen Schritten auf dem Weg zur Klassenkorpertheorie Rechnung zu tragen. Die Anhange von O. Taussky bilden eine wertvolle Erganzung des Buches. ARTINs Vorlesungen von 1932, deren Ubersetzung auf einem Manuskript basiert, das die Autorin 1932 selbst aus ihrer Vorlesungsnachschrift erarbeitete und von H. HASSE durchgesehen sowie mit Hinweisen versehen wurde, durfte fur Mathematiker und Mathematikhistoriker gleichermassen von Interesse sein..." NTM- Schriftenreihe fur Geschichte der Naturwissenschaften, Technik und Medizin

Table of Contents:
I. Preliminaries.- 1. Introductory Remarks on Quadratic Forms.- 2. Algebraic Background.- 3. Quadratic Euclidean Rings.- 4. Congruence Classes.- 5. Polynomial Rings.- 6. Dedekind Domains.- 7. Extensions of Dedekind Domains.- 8. Rational and Elliptic Functions.- II. Ideal Structure in Number Fields.- 9. Basis and Discriminant.- 10. Prime Factorization.- 11. Units.- 12. Geometry of Numbers.- 13. Finite Determination of Class Number.- III. Introduction to Class Field Theory.- 14. Quadratic Forms, Rings and Genera.- 15. Ray Class Structure and Fields, Hilbert Class Fields.- 16. Hilbert Sequences.- 17 Discriminant and Conductor.- 18. The Artin Isomorphism.- 19. The Zeta-Function.- Appendices (by Olga Taussky).- Lectures on Class Field Theory by E. Artin (Göttingen 1932) Notes by O. Taussky.- into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky).- Subject Matter Index.


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Product Details
  • ISBN-13: 9780387903453
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 328
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 0387903453
  • Publisher Date: 21 Sep 1978
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Series Title: Universitext


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A Classical Invitation to Algebraic Numbers and Class Fields: (Universitext)
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