Definition:Left Cancellable Operation

Definition
Let $\left ({S, \circ}\right)$ be an algebraic structure.

The operation $\circ$ in $\left ({S, \circ}\right)$ is left cancellable iff:
 * $\forall a, b, c \in S: a \circ b = a \circ c \implies b = c$

That is, iff all elements of $\left ({S, \circ}\right)$ are left cancellable.

Also see

 * Right Cancellable Operation
 * Cancellable Operation