New posts in Principal Ideal Domains

Prime elements in $\mathbb{Z}[\sqrt{2}]$

Is $\mathbb{Z}[x]$ a principal ideal domain?

number of element in a principal ideal domain can be $25/36/35/15$?

Smith Normal Form for PIDs

An integral domain whose every prime ideal is principal is a PID

A subring of the field of fractions of a PID is a PID as well.

Isomorphism of direct sums $R/a \oplus R/b \cong R/{\rm lcm}(a,b)\oplus R/\gcd(a,b)$

Show that every ideal of the ring $\mathbb Z$ is principal

Prove that a UFD is a PID if and only if every nonzero prime ideal is maximal