Definition:Simple Algebraic Field Extension

Definition

Let $F$ be a field.

Let $z$ be a complex number which is algebraic over $F$.

Then the smallest field $\map F z$ containing $F$ and $z$ is known as a simple algebraic (field) extension of $F$.

Also see

• Definition:Simple Field Extension

Sources

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