recently I am reading a paper on pfister forms in characteristic 2 and stumbled across a notation I do not know. It can be found here
Suppose $k$ is an arbitrary field of characteristic 2. Let $K:=k(\sqrt{\alpha_1},...,\sqrt{\alpha_n})$ be a field of dimensiom $2^n$ over $k$ such that $K^2 \subseteq k$. What does the $K^2$ mean in this case?
Thanks
slinshady
The squares in $K$.
Using that $k$ is of characteristic $2$, you can show that if $K$ is an extension of $k$ generated by square roots of elements in $k$ (like in your case), then every square of element in $K$ is in $k$. This is very specific to characteristic $2$: think of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ and $x = \sqrt{2} + \sqrt{3}$.