Frobenius extensions of QF-3 rings

Abstract

We investigate the inheritance of QF-3 property for ring extensions, mainly, for Frobenius extensions. Let A be a ring with identity. It is proved that a group ring A [ G ] A[G] of A with a finite group G is left QF-3 iff A is left QF-3 and that in case A is a. G-Galois extension of the fixed subring A G {A^G} relative to a finite group G of ring automorphism of A, A is left QF-3 iff A G {A^G} is left QF-3.