On a theorem from Skew field constructions
P. M. Cohn
Proc. Amer. Math. Soc. 84 (1982), 1-7
Primary 16A39; Secondary 16A06
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Abstract: Let be a skew field and a central subfield, then the free -field on centralizing is denoted by . The object is to prove the following theorem. Let be a skew field with a central subfield , let be a subfield of and put ; then there is a natural embedding of in if and only if and are linearly disjoint over .
This result replaces the erroneous Theorem 6.3.6 on p. 148 of the author's Skew field constructions, a counterexample to the latter (due to G. M. Bergman) is also described. The paper also includes an improved form of the specialization lemma (1.c.).
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