QTAG-modules having all high submodules relative closure

Abstract

This article is concerned with the investigation of two questions. The first question is: What QTAG-modules M with M¹=0 are direct summands of all QTAG-modules containing them as high submodules? The second question is the following: What are the submodules whose relative closures are large submodules? In addition, a necessary and sufficient condition for a submodule to be h-pure-absolute summand is obtained.