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Nov 29, 2011 at 13:50 comment added Georges Elencwajg Dear Hagen, thank you for your thoughtful answer: your remark on the separable algebraic case is quite relevant. That the the tensor product of a separable algebraic extension K and a purely inseparable extension L is a field follows from A sufficient condition in the question since a purely inseparable extension is trivially primary.
Nov 29, 2011 at 11:37 history answered Hagen CC BY-SA 3.0