◀ ▲ ▶Branches / Algebra / Proposition: Principal Ideal Generated by A Unit
The following proposition is a generalization of how to create a reduced residue system of integers from others".
Proposition: Principal Ideal Generated by A Unit
An element $c$ is a unit of an integral domain $(R, + ,\cdot)$ if and only if the principal ideal $(c)$ equals the whole domain $R$; formally $$c\in R^\ast\Longleftrightarrow ( c )=R.$$
Table of Contents
Proofs: 1 2 3
Thank you to the contributors under CC BY-SA 4.0!
- Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013