7 problems

Let $G$ be a group. Its integral group ring is denoted by $\mathbb{Z}G$. Baer's conjecture. $\mathbb{Z}G$ is Noetherian if and only if $G$ is virtually polycyclic. The forward i…

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 $K$ 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…

Skryabin's conjecture. The antipode $S$ is bijective.

Let $R$ be an excellent Noetherian ring of finite Krull dimension, and let $N\subseteq M$ be finitely generated $R$-modules. Huneke's uniform Artin–Rees conjecture. There exists an…

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…

Let $k$ be an algebraically closed field of characteristic $0$, and let $A$ be a finitely generated $k$-algebra that is a domain of quadratic growth. Suppose that $A$ does not sati…