Tensor products of division rings and finite generation of subfields
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- by Richard Resco, Lance W. Small and Adrian R. Wadsworth PDF
- Proc. Amer. Math. Soc. 77 (1979), 7-10 Request permission
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
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 7-10
- MSC: Primary 16A39; Secondary 16A08, 16A33, 16A45
- DOI: https://doi.org/10.1090/S0002-9939-1979-0539619-5
- MathSciNet review: 539619