Abstract
Let D be a division algebra over a field k. It is shown that if D ⊗ k D 0 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 {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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