2 problems

Atomic integral-extension boundary conjecture. If $S$ is atomic, then $S$ cannot contain a nonunit of boundary $0$.

Let $K$ be a real quadratic field and, for each positive integer $f$, let $\mathcal{O}_f=\mathbb{Z}+f\mathcal{O}_K$ be the order of conductor $f$. A domain is half-factorial if eve…