show/hide this revision's text 2 trivial formatting error corrected

One of your questions does have a positive answer.

  • Is there a purely algebraic way to distinguish between the splitting fields of $x^2+2$ and $x2−2$?x^2−2$?

The field $Q(\sqrt 2)$ can be ordered while the field $Q(i\sqrt 2)$ can not since -1 is a sum of squares.
show/hide this revision's text 1

One of your questions does have a positive answer.

  • Is there a purely algebraic way to distinguish between the splitting fields of $x^2+2$ and $x2−2$?

The field $Q(\sqrt 2)$ can be ordered while the field $Q(i\sqrt 2)$ can not since -1 is a sum of squares.