Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a theorem from Skew field constructions


Author: P. M. Cohn
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A39, 16A06

Retrieve articles in all journals with MSC: 16A39, 16A06


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633265-0
Keywords: Skew field (division ring), centre, linearly disjoint, full, honest, semifir, fir, Ore domain, quaternions, specialization lemma
Article copyright: © Copyright 1982 American Mathematical Society