Properties of a (general) field $F$ Let $F$ be a field and $E/F$ a field extension. Commutative ring $R (\neq 0)$ is a field $\Leftrightarrow$ Ideals of $R$ are only $0\left(=(0)\right)$ or $R\left(=(1)\right)$ Proof. $(\Rightarrow):\,a\in…