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