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seen Jul 14 '13 at 10:00

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comment least prime in a arithmetic progression
In fact, the Bach-Sorenson bound has been improved. See math.uiuc.edu/~xiannan/QuaResL1ver2.pdf
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comment When is the tensor product of two fields a field?
Dear Georges, I was actually suggesting to use Prop 107 of Pete's notes, if linear disjointness is considered well-understood.
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comment When is the tensor product of two fields a field?
Is linear disjointness considered a well-understood condition? If so, it suffices to check that images of $K$ and $L$ in $E$ are linearly disjoint for any extension $K,L \to E$. For this we can check dimensions as Ralph said, at least for finite extensions.
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