13 problems

The catenary-degree equality conjecture. For every group $G$ with

Half-factorial class-group conjecture. For every abelian group $G^*$, there exists a half-factorial Krull monoid, equivalently a half-factorial Dedekind domain, whose class group i…

Let $G$ be an abelian group. A Krull monoid is half-factorial if every nonunit has all its factorizations of the same length; a Dedekind domain is half-factorial when its multiplic…

Tame-degree conjecture. One has

Characterization conjecture. If

Let $H$ be a Krull monoid with finite class group $G$, and let … be its system of sets of lengths, where $\mathsf L(a)$ is the set of factorization lengths of $a$. The system…

Geroldinger–Grynkiewicz–Yuan conjecture. There exists some $k^{\ast}\in\mathbb{N}$ such that, for every $k\ge k^{\ast}$,

Let $H$ be a Krull monoid with finite noncyclic class group $G$, where every class contains a prime divisor. For $k\in\mathbb N$, let $\mathcal U_k(H)$ be the union of all sets of…

Let $H$ and $H'$ be Krull monoids with finite class groups $G$ and $G'$, respectively, such that $|G|\ge |G'|\ge 4$ and every class contains a prime divisor. Write…

Let $H$ be a Krull monoid as in Theorem 5.3, with associated set $G_P$, and suppose in addition that … For $k\in\mathbb N$, let $\mathcal U_k(H)$ denote the union of the sets of le…

Distinctness conjecture. The systems of sets of lengths are always distinct:

Half-factorial class-group conjecture. Every abelian group is the class group of a half-factorial Krull monoid.

Infinite-group half-factoriality conjecture. For every infinite abelian group $G$, there is a Krull monoid with class group $G$ and set $G_{mathcal P}$ such that every set of lengt…