4 problems

Costa's second conjecture. The $(n,d)$-property and the weak $(n,d)$-property are equivalent for every pair of nonnegative integers $n$ and $d$.

Let $A$ be a connected finitely generated ${\mathbb N}$-graded algebra over a field $k$, with $A_0=k$. The algebra $A$ is graded coherent if every finitely generated graded ideal i…

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…

Strictness conjecture. The class of all rings characterized by Theorem closureprodd is strictly bigger than the class of all left strongly coherent rings.