Definition:Primitive Element

This page is about primitive element. For other uses, see primitive.

Definition

Primitive Element of Cyclic Modulo Group

Let $p$ be a prime number.

Let $\Z'_p$ denote the cyclic multiplicative group of reduced residues of order $p - 1$.

Let $a$ be a generator of $\Z'_p$.

Then $a$ is known as a primitive element of $\Z'_p$.

Primitive Element of Field Extension

Let $F / K$ be a simple field extension such that $F = \map K \alpha$.

Then $\alpha$ is a primitive element of $F$.

Also see

• Results about primitive elements can be found here.