ON THE LATTICE R-TORS FOR SEMIPERFECT AND QF RINGS

Abstract

We define the equivalence relation approximately F in R-tors by tau approximately F-sigma iff the class of tau-codivisible modules coincides with the class of sigma-codivisible modules. We define the equivalence relation approximately T in R-tors by tau approximately T-sigma iff the class of tau-injective modules coincides with the class of sigma-injective modules. We prove that each equivalence class [tau] is-an-element-of R-tors/approximately F is a complete sublattice of R-tors when R is a semiperfect ring. We also prove that the equivalence relations approximately F and approximately T coincide for QF-rings.