3 problems

Topological perfectness conjecture. A topological ring $\mathfrak R$ is topologically left perfect if and only if it is topologically right coperfect.

Contramodule Bass-flat equivalence conjecture. The following conditions are equivalent to each other and to the conditions listed in the theorem: (i$^\flat$) all Bass flat left…

Semiperfect quasi-$\pi_\infty$-regularity conjecture. Then $R$ is semiperfect and quasi-$\pi_\infty$-regular with respect to some topology. The condition on $J$ ensures that the to…