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The structure of alternative division rings


Authors: R. H. Bruck and Erwin Kleinfeld
Journal: Proc. Amer. Math. Soc. 2 (1951), 878-890
MSC: Primary 09.1X
DOI: https://doi.org/10.1090/S0002-9939-1951-0045099-9
MathSciNet review: 0045099
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  • [1] A. A. Albert, On ordered algebras, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 521-522. MR 0001972 (1:328e)
  • [2] -, Absolute-valued algebraic algebras, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 763-768. MR 0030941 (11:76h)
  • [3] L. E. Dickson, On quaternions and their generalizations and the history of the eight square theorem, Ann. of Math. (2) vol. 20 (1919) pp. 155-171. MR 1502549
  • [4] Marshall Hall, Projective planes, Trans. Amer. Math. Soc. vol. 54 (1943) pp. 229-277. MR 0008892 (5:72c)
  • [5] Ruth Moufang, Zur Struktur der projektiven Geometrie der Ebene, Math. Ann. vol. 105 (1931) pp. 536-601. MR 1512725
  • [6] -, Die Einführung der idealen Elemente in die ebene Geometrie mit Hilfe des Satzes vom vollständigen Vierseit, Math. Ann. vol. 105 (1931) pp. 579-778.
  • [7] -, Die Schnittpunktsätze des projektiven speziellen Fünfecksnetzes in ihrer Abhängigkeit voneinander (Das A-Netz), Math. Ann. vol. 106 (1932) pp. 755-795. MR 1512782
  • [8] -, Ein Satz über die Schnittpunktsätze des allgemeinen Fünfecksnetzes (Das (A, B)-Netz), Math. Ann. vol. 107 (1933) pp. 124-139. MR 1512792
  • [9] -, Die Desarguesschen Sätze vom Rang 10, Math. Ann. vol. 108 (1933) pp. 296-310. MR 1512850
  • [10] -, Alternativkörper und der Satz vom vollständigen Vierseit $ ({D_9})$, Abh. Math. Sem. Hamburgischen Univ. vol. 9 (1933) pp. 207-222.
  • [11] -, Zur Struktur von Alternativkörpern, Math. Ann. vol. 110 (1934) pp. 416-430.
  • [12] R. D. Schafer, Alternative algebras over an arbitrary field, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 549-555. MR 0008610 (5:33d)
  • [13] M. F. Smiley, The radical of an alternative ring, Ann. of Math. (2) vol. 49 (1948) pp. 702-709. MR 0025449 (10:6f)
  • [14] -, Some questions concerning alternative rings, Bull. Amer. Math. Soc. vol. 57 (1951) pp. 36-43. MR 0038950 (12:473h)
  • [15] Max Zorn, Theorie der alternativen Ringe, Abh. Math. Sem. Hamburgischen Univ. vol. 8 (1930) pp. 123-147.

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DOI: https://doi.org/10.1090/S0002-9939-1951-0045099-9
Article copyright: © Copyright 1951 American Mathematical Society

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