Definition:Left Cancellable Operation

Definition
Let $\struct {S, \circ}$ be an algebraic structure.

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

That is, all elements of $\struct {S, \circ}$ are left cancellable.

Also see

 * Definition:Right Cancellable Operation
 * Definition:Cancellable Operation