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A module  over an associative ring  with unity is a QTAG module if every finitely generated submodule of any homomorphic image of  is a direct sum of uniserial modules. There are many fascinating properties of QTAG modules of which -pure submodules and high submodules are significant. A submodule  is quasi--dense in  if  is -divisible, for every -pure submodule  of  containing  Here we study these submodules and obtain some interesting results. Motivated by -neat envelope, we also define -pure envelope of a submodule  as the -pure submodule  if  has no direct summand containing  We find that -pure envelopes of  have isomorphic basic submodules, and if  is the direct sum of uniserial modules, then all -pure envelopes of  are isomorphic

algerba/algebra

On Quasi-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:math>-Dense Submodules and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:math>-Pure Envelopes of QTAG Modules

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