Definition:Algebraic Number over Field/Degree
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Definition
Let $F$ be a field.
Let $z \in \C$ be algebraic over $F$.
The degree of $\alpha$ is the degree of the minimal polynomial $\map m x$ whose coefficients are all in $F$.
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions