# Cancellative

## Definition

Let $$(M, *)$$ be a magma. Then $$(M,*)$$ is a cancellative magma if and only if

$$*$$ is left cancellative
$$\forall a,b,c \in S : ab = ac \Rightarrow b = c$$
$$*$$ is right cancellative
$$\forall a,b,c \in S : ba = ca \Rightarrow b = c$$