Contramodules over pro-perfect topological rings

For four wide classes of topological rings $\mathfrak R$, we show that all flat left R$-contramodules have projective covers if and only are descending chains cyclic discrete right R$-modules terminate the quotient R$ perfect. Three for which this holds complete, separated associative with a base neighborhoods zero formed by open two-sided ideals such either ring is commutative, or it has countable zero, finite number semisimple rings. The fourth class consists closed ideal certain properties product from previous three classes. key technique on proofs based contramodule Nakayama lemma topologically T-nilpotent ideals.