Abstract
We define the equivalence relation in R-tors by iff the class of τ-codivisible modules coincides with the class of σ-codivisible modules. We define the equivalence relation in R-tors by τ σ iff the class of τ-injective modules coincides with the class of σ-injective modules. We prove that each equivalence class is a complete sublattice of R-tors when R is a semiperfect ring. We also prove that the equivalence relations coincide for QF-rings.
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