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-...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.展开更多
文摘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.
