# Definition:Galois Field

## Definition

A **Galois field** $\struct {F, +, \circ}$ is a field such that $F$ is a finite set.

The symbol conventionally used to denote a Galois field is $\F$.

## Also known as

Some sources do not mention Galois, but merely refer to a **finite field**.

Some sources use the notation $\map {\operatorname {GF} } n$ to denote a **Galois field** of order $n$.

## Also see

- Results about
**Galois fields**can be found here.

## Source of Name

This entry was named for Évariste Galois.

## Technical Note

The $\LaTeX$ code for \(\F\) is `\F`

or `\FF`

.

## Sources

- 1964: Iain T. Adamson:
*Introduction to Field Theory*... (previous) ... (next): $\S 1.1$ - 1978: John S. Rose:
*A Course on Group Theory*... (previous) ... (next): $0$: Some Conventions and some Basic Facts