International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 801-814

Tag-modules with complement submodules H-pure

Surjeet Singh1,3 and Mohd Z. Khan2

1Department of Mathematics, Kuwait university, PO Box 5969, Safat 13060, Kuwait
2Deparent of Mathematics, Aligarh Muslim university, Aligarh 202001, U.P., India
3Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 5 February 1996; Revised 11 August 1997

Copyright © 1998 Surjeet Singh and Mohd Z. Khan. 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.


The concept of a QTAG-module MR was given by Singh [8]. The structure theory of such modules has been developed on similar lines as that of torsion abelian groups. If a module MR is such that MM is a QTAG-module, it is called a strongly TAG-module. This in turn leads to the concept of a primary TAG-module and its periodicity. In the present paper some decomposition theorems for those primary TAG-modules in which all h-neat submodules are h-pure are proved. Unlike torsion abelian groups, there exist primary TAG-modules of infinite periodicities. Such modules are studied in the last section. The results proved in this paper indicate that the structure theory of primary TAG-modules of infinite periodicity is not very similar to that oftorsion abelian groups.