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Subfield
Definition
$\langle F,+,*\rangle \in \mathrm{field}(F) $ |
$\langle \hat F,\hat +,\hat*\rangle\in\mathrm{subfield}(\langle F,+,*\rangle) $ |
$ 0,1\in \hat F $ |
$x,y\in \hat F$ |
$ x+y,\ x*y,\ x-y,\ x*y^{-1}\in \hat F $ |
$ x\ \hat +\ y,\ x\ \hat *\ y,\ x\ \hat -\ y,\ x*y^{\hat{-1}} \in \hat F $ |
Discussion
Reference
Wikipedia: Field