Is $\mathbb{Q}$ a principal ideal domain? I know that $\mathbb{Z}$ is, but I'm not sure about $\mathbb{Q}$.
Asked
Active
Viewed 744 times
1 Answers
5
Yes, it is. Every field is a principal ideal domain, since it has no non-trivial ideals.
J.R.
- 17,904
-
More precisely, the ideals of a field are all principal: $(0)$, $(1)$. – lhf Nov 22 '15 at 10:06