Torsion theories of quasi-frobenius extensions

摘要

For a given ringR, letQr(R) (resp.Ql(R)) denote the maximal right (resp. left) quotient ring ofR. It is shown that ifAis a finite normalizing quasi-Frobenius extension ofB, thenQr(A) =Ql(A) if and only ifQr(B) =Ql(B).