The ordinary quaternions over a Pythagorean field
Authors: Burton Fein and Murray Schacher
Journal: Proc. Amer. Math. Soc. 60 (1976), 16-18
MSC: Primary 12D15; Secondary 12A80, 16A40
MathSciNet review: 0417139
Abstract: Let L be a proper finite Galois extension of a field K and let D be a division algebra with center K. If every subfield of D properly containing K contains a K-isomorphic copy of L, it is shown that K must be Pythagorean, , and D is the ordinary quaternions over K. If one assumes only that every maximal subfield of D contains a K isomorphic copy of L, then, under the assumption that [D : K] is finite, it is shown that K is Pythagorean, , and D contains the ordinary quaternions over K.
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