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Axiomatic characterization of fields by the product formula for valuations


Authors: Emil Artin and George Whaples
Journal: Bull. Amer. Math. Soc. 51 (1945), 469-492
DOI: https://doi.org/10.1090/S0002-9904-1945-08383-9
This work is cited by: Bull. Amer. Math. Soc., Volume 52, Number 4 (1946), 245--247
This work is cited by: Bull. Amer. Math. Soc., Volume 53, Number 4 (1947), 377--380
MathSciNet review: 0013145
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    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.
  • C. Chevalley, La théorie du corps de classes, Ann. of Math. (2) 41 (1940), 394–418 (French). MR 2357, DOI https://doi.org/10.2307/1969013
  • Alexander Ostrowski, Über einige Lösungen der Funktionalgleichung $\psi (x)\cdot \psi (x)=\psi (xy)$, Acta Math. 41 (1916), no. 1, 271–284 (German). MR 1555153, DOI https://doi.org/10.1007/BF02422947
  • 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.
  • George Whaples, Non-analytic class field theory and Grünwald’s theorem, Duke Math. J. 9 (1942), 455–473. MR 7010


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