13 problems

Let $K$ be a field of characteristic zero, let $\mathfrak{g}$ be a Lie algebra over $K$, and let $U(\mathfrak{g})$ denote its universal enveloping algebra. Sierra–Walton conjecture…

Let $R[G]$ denote the group ring of a group $G$ over a ring $R$. Baer's conjecture. The group ring $R[G]$ is Noetherian if and only if $G$ is virtually polycyclic. The source state…

Redundancy conjecture. This assumption is redundant both in item (2) of the paper's main theorems and, in general, in the main theorems of Joel's cited works.

Let $S$ be an affine semigroup with standard expression, and let $S_2$ be the semigroup appearing in the standard expressions of $S$ and $S_2$ referenced in the source. Write…

Let $A$ be a finite subset of a lattice, let ${\mathbb N}A$ be the affine semigroup it generates, and let $S_c({\mathbb N}A)$ be its scored closure. Suppose its irredundant standar…

A graded algebra $A$ is regular if it has finite global dimension $d$ and satisfies the Gorenstein condition … The algebras of polynomial growth are called Artin–Schelter (AS) regu…

Simplicity conjecture. The group $\widehat{G}$ is simple.

Noetherian group-algebra conjecture. If $kG$ is noetherian, then $G$ is polycyclic-by-finite.

Let $A$ and $B$ be derived equivalent noetherian rings, and let ${\rm del}(A)$ and ${\rm del}(B)$ denote their delooping levels. The delooping-finiteness conjecture. One has … This…

Closed-point hull conjecture. Every closed point of $\operatorname{InjSpec}(R)$ is the injective hull of a simple $R$-module.

Let $R$ be a noetherian ring of finite dimension. Finiteness conjecture. The integral dimension satisfies … The paper establishes finiteness for several large classes, including no…

Let $G$ be a group and let $k[G]$ denote its group algebra over a field $k$. The Hall conjecture. The group algebra $k[G]$ is noetherian if and only if the underlying group $G$ is…

Let ${\Bbbk}$ be a field of characteristic $0$, let $L$ be a Lie algebra over ${\Bbbk}$, and let $U(L)$ denote its universal enveloping algebra. Finite-dimensionality conjecture. A…