Definition:Regular Representations/Right Regular Representation

Definition
Let $\left ({S, \circ}\right)$ be an algebraic structure. The mapping $\rho_a: S \to S$ is defined as:


 * $\forall a \in S: \rho_a \left({x}\right) = x \circ a$

This is known as the right regular representation of $\left ({S, \circ}\right)$ 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
Although the right regular representation is defined here in the context of the general algebraic structure, many treatments of abstract algebra define this construct only for semigroups.

Also see

 * Left Regular Representation


 * Regular Representations of Invertible Elements are Permutations
 * Regular Representations in Group are Permutations