New posts in unique-factorization-domains

Unique factorization domain and principal ideals

Irreducibles are prime in a UFD

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

Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain

Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.

Where Fermat's last theorem fails

Principal prime ideals are minimal among prime ideals in a UFD

Ring of integers is a PID but not a Euclidean domain

Motivation for Eisenstein Criterion

Does $A$ a UFD imply that $A[T]$ is also a UFD?

One-dimensional [Noetherian] UFD is a PID

About the localization of a UFD

Ring of trigonometric functions with real coefficients

Motivation behind the definition of GCD and LCM

Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?