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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tensor products of division rings and finite generation of subfields


Authors: Richard Resco, Lance W. Small and Adrian R. Wadsworth
Journal: Proc. Amer. Math. Soc. 77 (1979), 7-10
MSC: Primary 16A39; Secondary 16A08, 16A33, 16A45
MathSciNet review: 539619
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Abstract: Let D be a division algebra over a field k. It is shown that if $ D{ \otimes _k}{D^0}$ is Noetherian, then every commutative subfield of D containing k is finitely generated over k. This theorem applies to $ {D_n}$, the quotient division algebra of the nth Weyl algebra, and also to a number of other standard examples of nonalgebraic division algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0539619-5
PII: S 0002-9939(1979)0539619-5
Keywords: Division rings, finitely generated subfields, Weyl algebras
Article copyright: © Copyright 1979 American Mathematical Society