List questions from principal-ideal-domains | MathQa

$x=(0,\overline{1})$ and $y=(0,\overline{2})$ generate the same ideal in $R=\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$

Published on 29 Dec 2024 - 9:05

How do I show that the unit group of $\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$ is a cyclic group of order 10?

Published on 12 Jan 2025 - 9:03

Is a localization of a UFD at a prime ideal a PID?

Published on 08 Jan 2025 - 22:09

Ideal class group of $ \mathbb{Z}[ \sqrt{2} ] $

Published on 29 Dec 2024 - 6:06

$R=\{a/b: a,b \in \mathbb{Z}$ and $b$ is odd}. Show that the ring $R$ is a PID.

Published on 06 Jan 2025 - 0:11

Is $\mathbb{Z}[\sqrt[3]{2}]$ a principal ideal domain?

Published on 03 Jan 2025 - 8:03

Finitely generated torsion free module over $A$ is locally free

Published on 31 Dec 2024 - 15:31

When is $\Bbb{Z}[\zeta_n]$ a PID?

Published on 12 Jan 2025 - 18:01

Find an Ideal of $\mathbb{Z}+x \mathbb{Q}[ x ]$ that is NOT principal

Published on 31 Dec 2024 - 10:30

Question in proving "Any principal ideal domain is a unique factorization domain"

Published on 02 Jan 2025 - 22:26