3 problems

Let $A$ be a relatively free profinite algebra, and let $\rho$ be a fully invariant closed congruence on $A$. Almeida–Klíma's profiniteness conjecture. The congruence $\rho$ is pro…

Let $A$ be a profinite algebra that is left semiartinian, equivalently semilocal with Jacobson radical $J$ right T-nilpotent. The semiartinian profinite algebra conjecture. The Jac…

Free profinite $\mathscr{D}$-monoid conjecture. The free profinite $\mathscr{D}$-monoid on $\Sigma$ arises as the limit of all quotient monoids of $\Psi\Sigma^*$.