Proof: By Induction
(related to Proposition: Principal Ideal Generated by A Unit)
- Let $( c )=R.$
- In particular, $1\in ( c ).$
- Therefore, there is an $b\in R$ with $bc=1.$
- Therefore, $c\in R^\ast.$
Thank you to the contributors under CC BY-SA 4.0!
- Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013