Definition:Cancellable Operation

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

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

That is, iff it is both a left cancellable operation and a right cancellable operation.

Also see

 * Definition:Right Cancellable Element
 * Definition:Left Cancellable Element


 * Definition:Cancellable Element