Tag-modules with complement submodules H-pure
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 T...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298001112 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |