This is a part of statement in the book I do not fully appreciate. Suppose $E/K$ is Galois extension and $G$ the Galois group of $E/K$. $E[G]$ is the group ring formed by finite group $G$.

*"It is worthwhile remarking that $E\otimes_KE\cong EG$ can be viewed as a deep reason why Galois theory works."* Ref: Algebra Vol 1: Fields and Galois Theory by Falko Lorenz.

**Q:** (solved by the comments below) What is the implication above? I thought $E\otimes_KE\cong EG$'s proof has a major ingredient that the trace map is non degenerate (i.e $E/K$ is separable). Is this affording some representation of $G\to \operatorname{Aut}_K(E)$? What is the author trying to express? Does this extend to infinite Galois extension case?

This question (**Q**) has been asked on Stackexchange ~~but there is no answer~~. Hence, I asked this on MO.

**Q':** As Qiaochu commented that this is related to torsor theory, I do not see why the two are related. It would be nice if someone could elaborate this a bit.

continuousfunctions ($G$ with the Krull topology and $K$ with the discrete topology). The title of his article is "The normal basis theorem for infinite extensions," or something close to that. $\endgroup$5more comments