The lattice $R$-tors for perfect rings

Abstract

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 .We describe the largest element in [r] as X(Rad R/t,(Rad R)) and the least element of [r] as 1(t r(RadR» .Using these results we give a necessary and sufficient condition for the central splitting of Goldman torsion theory when R is semiperfect.We prove that for a QF ring R the least element of [X]^'F is the Goldie torsion theory.This can be used to prove that for a QF ring ^'F and -T are equal, where r ^'T o iff the class of r-injective modules coincides with the class of v-injective modules .

Locations

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