On Quasi-h-Dense Submodules and h-Pure Envelopes of QTAG Modules

Abstract EN

A 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.

There are many fascinating properties of QTAG modules of which h-pure submodules and high submodules are significant.

A submodule N is quasi-h-dense in M if M/K is h-divisible, for every h-pure submodule K of M, containing N.

Here we study these submodules and obtain some interesting results.

Motivated by h-neat envelope, we also define h-pure envelope of a submodule N as the h-pure submodule K⊇N if K has no direct summand containing N.

We find that h-pure envelopes of N have isomorphic basic submodules, and if M is the direct sum of uniserial modules, then all h-pure envelopes of N are isomorphic.