7 problems

Principal-plinth-ideal conjecture.

Invariant-coordinate conjecture. For every such $\phi$, there exists $\sigma\in\operatorname{T}_3(k)$ such that

Let $R=D(\sigma,a)$ be a quantum generalized Weyl algebra, and let $\phi=\eta_{\gamma,\mu}$ be a finite-order diagonal automorphism as in Corollary 1, with…

Let $R$ be a coherent regular ring, and let $G$ be a group of automorphisms of $R$. Write $R^G$ for the ring of invariants, and suppose that $R^G$ is a module retract of $R$ and th…

Wehlau et al.'s degree bound conjecture. The quotient ring $\Bbbk[V]^G/I$ is generated by invariants of degree at most $|G|$.

Glaz's existence problem. Can one define non-Noetherian Cohen–Macaulay rings so that: (i) the definition agrees with the usual definition for Noetherian rings; (ii) coherent regula…

Let $k$ be a field of characteristic zero and let $A=k[X_1,\ldots,X_{n+1}]$. For $D_1,\ldots,D_n\in\operatorname{LND}(A)$, write … A polynomial $f\in A$ is a coordinate if it is pa…