Abstract
A right module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.This article considers the closure of h-pure-S-high submodules of QTAG-modules.Here,we determine all submodules S of a QTAG-module M such that each closure of h-pure-S-high submodule of M is h-pure-(S)-high in (M).A few results of this theme give a comparison of some elementary properties of h-pure-S-high and S-high submodules.
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