Semiprimary selfinjective algebras with at most countable dimensional Jacobson quotient are QF

英文摘要：

We give a positive answer to a conjecture of Faith stating that a self-injective semiprimary ring is QF, for algebras which are at most countable dimensional modulo their Jacobson radical. As a consequence of the method used, we also give short proofs of several other known positive cases of this conjecture.