Definition:Cancellable Monoid

Definition
Let $\struct {S, \circ}$ be a monoid.

$\struct {S, \circ}$ is defined as being cancellable :


 * $\forall a, b, c \in S: a \circ c = b \circ c \implies a \circ b$
 * $\forall a, b, c \in S: a \circ b = a \circ c \implies b \circ c$

That is, $\circ$ is a cancellable operation.