Definition:Regular Representations/Right Regular Representation
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Definition
Let $\left ({S, \circ}\right)$ be a semigroup.
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 $a$.
Sources
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 35$
