New posts in Principal Ideal Domains

Proving a subring of $\Bbb Z[\zeta_{11}]$ is PID

Gaussian Integers form an Euclidean Ring

All $\mathbb{Z}$-submodules of $\mathbb{Z}\oplus\mathbb{Z}$ are free.

Is every PID a UFD?

Is $\mathbf{Z}[X]/(2,X^2+1)$ a field/PID?

Krull dimension of polynomial rings over noetherian rings

One-dimensional [Noetherian] UFD is a PID

In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?

Ring of integers is a PID but not a Euclidean domain

Prove that $n^2+n+41$ is prime for $n<40$