This paper continues the study of the existence of torsion-free covers with respect to a faithful hereditary torsion theory (ℑ,F) of left modules over a ringR with unity. If the filter of left ideals associated with (ℑ,F) has a cofinal subset of finitely generated left ideals, then every leftR-module has a torsion-free cover. An example is given to illustrate how this result generalizes all previously known existence theorems for torsion-free covers.
KeywordsLeft Ideal Injective Module Semiprime Ring Torsion Theory Left Module
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