4 added new tag (characteristic p)
3 edited tags
2 edited body

Can someone verify this for me.. or tell me what reference shows me this... is this true:

Let k be a field then a field extension K of k is separable over k iff

for any field extension L >= k the Jacobian Jacobson radical of the tensor product K (x)_k L is trivial.

I got this idea by looking at some definitions of separable algebras (which is not my field of research.. but somehow this definition got me intruiged). Anyone knows if this is true and why so? or maybe a reference or two about it?

1