The Lift and Drag Functions for an Elastic Fluid in Two Dimensional Irrotational Flow.

bras of index m = 3. Here we have to consider only the linear equation P1 = 0 in (6). Without any further adjunction, we obtain an element A * 0 in D, with a characteristic equation x3 h3 = 0. This gives Wedderburn's result that all normal division algebras of index 3 are cyclic. In the case m = 4, we again consider only the equation P1 = 0 instead of (6). We obtain an element A * 0 in D, which has a characteristic equation of the formx4 h2x2-h4 = 0. The construction of such an element A forms the main part of Albert's proof of the theorem that every normal division algebra of index m = 4 possesses a Galois splitting field of degree 4 and can, therefore, be written as a crossed product, provided the characteristic of F is different from 2. 1 For references to the theory of algebras, cf. M. Deuring's book: Algebren (Ergebnisse der Mathematik, Berlin, 1935). 2 J. L. M. Wedderburn, Trans. Amer. Math. Soc., 22, 129 (1931). 3A. A. Albert, Trans. Amer. Math. Soc., 31, 253 (1929) and Bull. Amer. Soc., 38, 703 (1932). 4 R. Brauer, Math. Zeitschr., 30, 79 (1929). 6 This can also be seen from general considerations concerning simple algebras, without using the explicit form (1) of the elements. 6 A. A. Albert, Trans. Amer. Math. Soc., 36, 885 (1934). For the case of a field F of characteristic 5, cf. A. A. Albert, Trans. Amer. Soc., 39, 183 (1936).