Talk:Tensor product of fields

This article currently doesn't give a clear definition of the tensor product of fields in one place. Some rearrangement is needed. Dmharvey 00:32, 15 April 2006 (UTC)

I would add in what I believe to be the definition for tensor product of fields, but I am not sure it is correct, so I thought I would run it through the discussion page before I (or someone) added it: If k is a subfield of L and E, then we can consider L and E as k-modules so the tensor product of fields is just the normal tensor product of modules taken over k. Is this definition correct?LkNsngth (talk) 01:31, 28 January 2009 (UTC)

That is part of it: it tells you the vector space structure over k. The product, to make it a k-algebra, is what you might call the "obvious thing", by way of a bilinear map, namely multiply tensors in the first component and the second component. The complaint seems to be in the dependence of that definition, from tensor products of R-algebras over any commutative ring. It would be harmless enough to copy the definition across. Charles Matthews (talk) 15:41, 28 January 2009 (UTC)

I'ld also like to see some rationalisation of composite field, compositum, linearly disjoint. Richard Pinch (talk) 14:52, 20 June 2008 (UTC)