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The lattice $R$-tors for perfect rings

The lattice $R$-tors for perfect rings

We define ^'F in R-tors by r ^'F a iff the class of r-codivisible modules coincides with the class of o-codivisible modules .We prove that if R is left perfect ring (resp .semiperfect ring then every [r1 p E R-tors/-F (resp .[X]F and KIF) is a complete sublattice of R-tors …