(related to Proposition: Generalization of Cancellative Multiplication of Integers)

- Assume, $ac=bc.$
- Because of the distributivity law in rings, it follows $(a-b)c=0.$
- By hypothesis, $(R, + ,\cdot)$ is an integral domain and $c\neq 0.$
- Therefore $a-b=0.$
- This is equivalent to $a=b.$

- Assume, $a=b.$
- Multiplication by $c$ gives us $ac=bc.$∎

**Modler, Florian; Kreh, Martin**: "Tutorium Algebra", Springer Spektrum, 2013