Bulletin of the American Mathematical Society

Axiomatic characterization of fields by the product formula for valuations

Emil Artin and George Whaples

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Article information

Source
Bull. Amer. Math. Soc., Volume 51, Number 7 (1945), 469-492.

Dates
First available in Project Euclid: 3 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183507128

Mathematical Reviews number (MathSciNet)
MR0013145

Zentralblatt MATH identifier
0060.08302

Citation

Artin, Emil; Whaples, George. Axiomatic characterization of fields by the product formula for valuations. Bull. Amer. Math. Soc. 51 (1945), no. 7, 469--492. https://projecteuclid.org/euclid.bams/1183507128


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References

  • 1. E. Artin, Über die Bewertungen algebraischer Zahlkörper, Journal für Mathematik vol. 167 (1932) pp. 157-159.
  • 2. C. Chevalley, Sur la théorie du corps de classes dans les corps finis et les corps locaux, Journal of College of Sciences, Tokyo, 1933, II, part 9.
  • 3. C. Chevalley, Généralization de la théorie de corps de classes pour les extensions infinies, Journal de mathématiques pures et appliquées (9) vol. 15 (1936) pp. 359-371.
  • 4. C. Chevalley, La théorie du corps de classes, Ann. of Math. vol. 41 (1940) pp. 394-418.
  • 5. A. Ostrowski, Über einige Lösungen der Funktionalgleichung Φ(x)Φ(y)=Φ(xy), Acta Math. vol. 41 (1918) pp. 271-284.
  • 6. A. Ostrowski, Untersuchung in der arithmetische Theorie der Körper, Parts I, II, and III, Math. Zeit. 39 (1935) pp. 269-321.
  • 7. B. L. van der Waerden, Moderne Algebra, vol. 1, 2d ed., Berlin, 1937.
  • 8. G. Whaples, Non-analytic class field theory and Grunwald's theorem, Duke Math. J. vol. 9 (1942) pp. 455-473.

See also

  • This work is cited by: E. Artin, G. Whaples. A note on axiomatic characterization of fields. Bull. Amer. Math. Soc., Volume 52, Number 4 (1946), 245--247.
  • This work is cited by: George Whaples. On a conjecture about infinite class fields. Bull. Amer. Math. Soc., Volume 53, Number 4 (1947), 377--380.