On a theorem from Skew field constructions
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.).
-  P. M. Cohn, Free rings and their relations, Academic Press, London-New York, 1971. London Mathematical Society Monographs, No. 2. MR 0371938
-  Paul Moritz Cohn, Algebra. Vol. 2, John Wiley & Sons, London-New York-Sydney, 1977. With errata to Vol. I. MR 0530404
-  Paul Moritz Cohn, Skew field constructions, Cambridge University Press, Cambridge-New York-Melbourne, 1977. London Mathematical Society Lecture Note Series, No. 27. MR 0463237
-  -, The universal field of fractions of a semifir. III (to appear).
-  P. M. Cohn and Warren Dicks, On central extensions of skew fields, J. Algebra 63 (1980), no. 1, 143–151. MR 568568, https://doi.org/10.1016/0021-8693(80)90029-0
- P. M. Cohn, Free rings and their relations, London Math. Soc. Monographs, No. 2, Academic Press, London and New York, 1971. MR 0371938 (51:8155)
- -, Algebra, vol. 2, Wiley, Chichester, 1977. MR 0530404 (58:26625)
- -, Skew field constructions, London Math. Soc. Lecture Notes, No. 27, Cambridge Univ. Press, Cambridge, 1977. MR 0463237 (57:3190)
- -, The universal field of fractions of a semifir. III (to appear).
- P. M. Cohn and W. Dicks, On central extensions of skew fields, J. Algebra 63 (1980), 143-151. MR 568568 (82m:16014)
Keywords: Skew field (division ring), centre, linearly disjoint, full, honest, semifir, fir, Ore domain, quaternions, specialization lemma
Article copyright: © Copyright 1982 American Mathematical Society