Kasyanyuk M. On QF- rings.

Dissertation is dedicated to research of quasi-Frobenius rings and serial quasi-Frobenius rings. Serial QF rings are characterized by the length composition of projective indecomposable modules, quasi-Frobenius rings and irreducible Frobenius semidistributive rings are constructed with any Nakayamapermutation. Subclasses of semi-perfect rings are introduced as generalization of the class of serial rings. Proved that serial rings are quasi-Frobenius if and only if all the homomorphisms of indecomposable projective modules have a nonzero kernel. We prove that any homomorphism of indecomposable projective modules over a quasi-Frobenius ring has a nonzero kernel. Proved that an indecomposable Artinian serial ring is а QF ring if and only if the quiver of this ring is a cycle and the lengths of all the major right and left modules are equal.