Definition:Right Operation

Definition

Let $S$ be a set.

For any $x, y \in S$, the right operation on $S$ is the binary operation defined as:

$\forall x, y \in S: x \to y = y$

Also see

It is clear that the right operation is the same thing as the second projection on $S \times S$:

$\forall \tuple {x, y} \in S \times S: \pr_2 \tuple {x, y} = y$

Also see

• Definition:Left Operation

• Results about right operation can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Example $2.4$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $5$: Semigroups: Exercise $3 \ \text{(i)}$