The following proposition is only a generalization of a cancelling rule when multiplying integers. In this sense, the ring of integers $(\mathbb Z, + ,\cdot)$ is only one special case of an integral domain, in which this law always holds.
Let $(R, + ,\cdot)$ be an integral domain. Then the multiplication operation "$\cdot$" is cancellative, i.e. for all $a,b,c\in R$ with $c\neq 0$ the following equivalence holds: $$ac=bc\Longleftrightarrow a=b.$$
Proofs: 1