Definition:Transcendental Number over Field
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Let $F$ be a field.
Let $z$ be a complex number.
$z$ is a transcendental number over $F$ if and only if $z$ cannot be expressed as a root of a polynomial with coefficients in $F$.
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions