Definition:Regular Representations/Right Regular Representation

Definition
Let $\struct {S, \circ}$ be a magma. The mapping $\rho_a: S \to S$ is defined as:


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

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 see

 * Definition:Left Regular Representation


 * Right Regular Representation of Subset Product


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