Definition:Cancellable Operation

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

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

That is, 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