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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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298001112 |
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| _version_ | 1832566770230099968 |
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| author | Surjeet Singh Mohd Z. Khan |
| author_facet | Surjeet Singh Mohd Z. Khan |
| author_sort | Surjeet Singh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-90172bc3d920459996014c31e9feb4de |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-90172bc3d920459996014c31e9feb4de2025-02-03T01:03:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121480181410.1155/S0161171298001112Tag-modules with complement submodules H-pureSurjeet Singh0Mohd Z. Khan1Department of Mathematics, Kuwait university, PO Box 5969, Safat 13060, KuwaitDeparent of Mathematics, Aligarh Muslim university, Aligarh, U.P. 202001, IndiaThe 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.http://dx.doi.org/10.1155/S0161171298001112QTAG-modulescomplement submodulesh-pure submodulesh-neat submodulesand basic submodules. |
| spellingShingle | Surjeet Singh Mohd Z. Khan Tag-modules with complement submodules H-pure International Journal of Mathematics and Mathematical Sciences QTAG-modules complement submodules h-pure submodules h-neat submodules and basic submodules. |
| title | Tag-modules with complement submodules
H-pure |
| title_full | Tag-modules with complement submodules
H-pure |
| title_fullStr | Tag-modules with complement submodules
H-pure |
| title_full_unstemmed | Tag-modules with complement submodules
H-pure |
| title_short | Tag-modules with complement submodules
H-pure |
| title_sort | tag modules with complement submodules h pure |
| topic | QTAG-modules complement submodules h-pure submodules h-neat submodules and basic submodules. |
| url | http://dx.doi.org/10.1155/S0161171298001112 |
| work_keys_str_mv | AT surjeetsingh tagmoduleswithcomplementsubmoduleshpure AT mohdzkhan tagmoduleswithcomplementsubmoduleshpure |