Artin, E.; Whaples, G. Axiomatic characterization of fields by the product formula for valuations. (English) Zbl 0060.08302 Bull. Am. Math. Soc. 51, 469-492 (1945). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 41 Documents Keywords:rings, modules, fields × Cite Format Result Cite Review PDF Full Text: DOI References: [1] E. Artin, Über die Bewertungen algebraischer Zahlkörper, Journal für Mathematik vol. 167 (1932) pp. 157-159. · JFM 58.0173.01 [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. · JFM 59.0190.01 [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. · Zbl 0015.15101 [4] C. Chevalley, La théorie du corps de classes, Ann. of Math. (2) 41 (1940), 394 – 418 (French). · JFM 66.0122.02 · doi:10.2307/1969013 [5] Alexander Ostrowski, Über einige Lösungen der Funktionalgleichung \?(\?)\cdot \?(\?)=\?(\?\?), Acta Math. 41 (1916), no. 1, 271 – 284 (German). · JFM 46.0169.02 · doi: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. · Zbl 0016.33902 [8] George Whaples, Non-analytic class field theory and Grünwald’s theorem, Duke Math. J. 9 (1942), 455 – 473. · Zbl 0063.08226 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.