Torsion theory extensions and finite normalizing extensions

Let S be a ring extension of R, and let tau(R) = (T(R), F(R)) and tau(S) = (T(S), F(S)) be torsion theories for right R-modules and right S-modules respectively. Using functors Hom(R)(-,S) and - circle times(R) S, we get the connection between tau(R) and tau(S), introduce torsion theory extensions related to ring extensions and establish some relations between finite normalizing extensions and torsion theory extensions. Furthermore, we consider some applications of torsion theory extensions and generalize some results of excellent extensions (almost excellent extensions) to the setting of torsion theories. (C) 2002 Elsevier Science B.V. All rights reserved.