Tensor products of division rings and finite generation of subfields
Tensor products of division rings and finite generation of subfields
Let <italic>D</italic> be a division algebra over a field <italic>k</italic>. It is shown that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D circled-times Subscript k Baseline upper D Superscript 0"> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation …