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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.

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

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Keywords: Division rings, finitely generated subfields, Weyl algebras
Article copyright: © Copyright 1979 American Mathematical Society