Definition:Transcendental Number over Field

Definition

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 $F$.

Also see

• Definition:Algebraic Number over Field

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions