On μ-complemented and singular modules

Abstract

In a previous paper we introduced μ-complemented modules for any given torsion functor μ of a hereditary torsion theory in Mod-R and presented their basic properties. Our current research enables us to characterize these modules when μ is a proper torsion theory other Than Goldie's and the ring is a one-dimensional Noetherian domain. The case in which μ has property (T) is also treated. For an arbitrary μ, rings for which every module is μ-complemented are considered.