On Modules Satisfying the Descending Chain Condition on Cyclic Submodules

A module satisfying the descending chain condition on cyclic submodules is called coperfect.The class of coperfect modules lies properly bet ween the class of locally artinian modules and the class of semiartinian modules.Let R be a commutative ring with identity.We show that every semiartinian Ti-module is coperfect if and only if R is a T-ring.It is also shown that the class of coperfect R-modules coincides with the class of locally artinian R-modules if and only if m/m^(2)is a finitely genera ted R-module for every maximal ideal m of R.