how I write in the title, studying the splitting field, I read there are a lot of extension of a field $\mathbb{K}$ in which $f(x)\in\mathbb{K}[x]$ can be write as a product of linear polynomials, minimal extension in the sense of inclusion. I know that this extensions are isomorphic, but I ask an example of two different extension.
Two different (isomorphic) splitting field
1
$\begingroup$
field-theory
extension-field
splitting-field
-
2Does something like $f(x) = x^2 - 2\in\Bbb Q[x]$ and the splitting fields $\Bbb Q[x]/(f(x))$ and $\Bbb Q(\sqrt{2})\subseteq\Bbb R$ satisfy you? – 2017-01-19
-
0I don't understand exactly what you mean by "different". – 2017-01-20
-
0Not equal, like the previuos example. – 2017-01-20