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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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