International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 801-814
doi:10.1155/S0161171298001112
Tag-modules with complement submodules H-pure
Surjeet Singh1
and M. Zubair Khan2
1Department of Mathematics, Kuwait university, PO Box 5969, Safat 13060, Kuwait
2Deparent of Mathematics, Aligarh Muslim university, Aligarh 202001, U.P., India
Abstract
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 M⊕M 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.