Modules satisfying the ascending chain condition on submodules with bounded uniform dimension

Abstract

We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is Noetherian. We investigate rings for which every module satisfies pand-acc and characterize the commutative rings with this property. It is proved that if R is a right Noetherian ring which is either right nonsingular or left Noetherian then every torsionless right R-module satisfies pand-acc. However, in general a direct product of simple modules need not satisfy pand-acc.