Definition:Field Adjoined Element

Definition
Let $E/F$ be a field extension, $\alpha \in E$.

Then:


 * $F[\alpha] $ denotes the smallest subring of $E$ containing $F \cup \alpha$.


 * $F(\alpha) $ denotes the smallest subfield of $E$ containing $F \cup \alpha$. We say this as $F$ adjoined with $\alpha$.