# Definition:Regular Representations/Right Regular Representation

## Definition

Let $\struct {S, \circ}$ be a magma.

The mapping $\rho_a: S \to S$ is defined as:

$\forall x \in S: \map {\rho_a} x = x \circ a$

This is known as the right regular representation of $\struct {S, \circ}$ with respect to $a$.

## Also known as

Some sources use a hyphen: right-regular representation.

However, this can be confusing: when the term right appears hyphenated in this manner, it usually has the meaning of perpendicular or orthogonal.

## Also defined as

Some treatments of abstract algebra and group theory define this construct for semigroups.

Some define it only for groups.

## Also see

• Results about regular representations can be found here.