# Cancellation law

In an algebraic structure $A$ with a binary operation $\cdot$, the left and right cancellation laws respectively hold if for all $x,y,z$ $$x \cdot y = x \cdot z \Rightarrow y = z \,,$$ $$x \cdot y = z \cdot y \Rightarrow x = z \ .$$ Such a structure is termed "cancellative".