-Regular Modules
We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to gen...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/630285 |
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| _version_ | 1832565631666356224 |
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| author | Areej M. Abduldaim Sheng Chen |
| author_facet | Areej M. Abduldaim Sheng Chen |
| author_sort | Areej M. Abduldaim |
| collection | DOAJ |
| description | We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to generalize pure submodules and proved that an -module is -regular if and only if every submodule of is -pure iff is a -regular -module for each maximal ideal of . Many characterizations and properties of -regular modules were given. An -module is -regular iff is a -regular ring for each iff is a -regular ring for finitely generated module . If is a -regular module, then . |
| format | Article |
| id | doaj-art-22c427c6f3804c649fcd5b45545adc9b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-22c427c6f3804c649fcd5b45545adc9b2025-02-03T01:07:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/630285630285-Regular ModulesAreej M. Abduldaim0Sheng Chen1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to generalize pure submodules and proved that an -module is -regular if and only if every submodule of is -pure iff is a -regular -module for each maximal ideal of . Many characterizations and properties of -regular modules were given. An -module is -regular iff is a -regular ring for each iff is a -regular ring for finitely generated module . If is a -regular module, then .http://dx.doi.org/10.1155/2013/630285 |
| spellingShingle | Areej M. Abduldaim Sheng Chen -Regular Modules Journal of Applied Mathematics |
| title | -Regular Modules |
| title_full | -Regular Modules |
| title_fullStr | -Regular Modules |
| title_full_unstemmed | -Regular Modules |
| title_short | -Regular Modules |
| title_sort | regular modules |
| url | http://dx.doi.org/10.1155/2013/630285 |
| work_keys_str_mv | AT areejmabduldaim regularmodules AT shengchen regularmodules |