(related to Proposition: Principal Ideal Generated by A Unit)

- Let $c$ is a unit of an integral domain $(R, + ,\cdot).$
- This means, there is a multiplicative inverse $b\in R$ with $bc=1.$
- Since $bc\in ( c ),$ we have $1\in ( c ).$
- Therefore $( c )=R.$

- Let $( c )=R.$
- In particular, $1\in ( c ).$
- Therefore, there is an $b\in R$ with $bc=1.$
- Therefore, $c\in R^\ast.$∎

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