Table of Contents
Volume 2013, Article ID 873193, 6 pages
Research Article

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

Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

Received 27 March 2013; Accepted 4 July 2013

Academic Editor: Antonio M. Cegarra

Copyright © 2013 Alveera Mehdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.