On a theorem from Skew field constructions
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- by P. M. Cohn PDF
- Proc. Amer. Math. Soc. 84 (1982), 1-7 Request permission
Abstract:
Let $F$ be a skew field and $C$ a central subfield, then the free $F$-field on $X$ centralizing $C$ is denoted by ${F_C}(X)$. The object is to prove the following theorem. Let $F$ be a skew field with a central subfield $C$, let $E$ be a subfield of $F$ and put $k = E \cap C$; then there is a natural embedding of ${E_k}(X)$ in ${F_C}(X)$ if and only if $E$ and $C$ are linearly disjoint over $k$. 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.).References
- P. M. Cohn, Free rings and their relations, London Mathematical Society Monographs, No. 2, Academic Press, London-New York, 1971. 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, London Mathematical Society Lecture Note Series, No. 27, Cambridge University Press, Cambridge-New York-Melbourne, 1977. 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, DOI 10.1016/0021-8693(80)90029-0
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 1-7
- MSC: Primary 16A39; Secondary 16A06
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633265-0
- MathSciNet review: 633265