Definition:Field Adjoined Element
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Definition
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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 $\alpha$.