On H-separable extensions of QF-3 rings

Abstract

Let a ring A be an H-separable extension of a subring B of A, that is, A ⊗ B A is an A-A-direct summand of a finite direct sum of copies of A. If furthermore, (a) B is a left B-direct summand of A (or (b) A is left B-finitely generated projective), and if B is a right (resp. left) artinian QF-3 ring, then A is also a right (resp. left) artinian QF-3 ring. Consequently, if A is an H-separable extension of a serial ring B with one of the conditions (a), (b), then A is also a serial ring. In particular H-separable extension of a uni-serial ring is always uni-serial.