δ-Small Submodules and δ-Supplemented Modules
Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an amply δ-supplemented module and satisfies DCC on...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/58132 |
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| _version_ | 1832550499036954624 |
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| author | Yongduo Wang |
| author_facet | Yongduo Wang |
| author_sort | Yongduo Wang |
| collection | DOAJ |
| description | Let R be a ring and M a
right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on
δ-small submodules; (3) M is Artinian if and only if M is
an amply δ-supplemented module and satisfies DCC on
δ-supplement submodules and on δ-small submodules. |
| format | Article |
| id | doaj-art-854daba39d3e4658b43c6f89fae5beac |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-854daba39d3e4658b43c6f89fae5beac2025-02-03T06:06:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/5813258132δ-Small Submodules and δ-Supplemented ModulesYongduo Wang0Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaLet R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an amply δ-supplemented module and satisfies DCC on δ-supplement submodules and on δ-small submodules.http://dx.doi.org/10.1155/2007/58132 |
| spellingShingle | Yongduo Wang δ-Small Submodules and δ-Supplemented Modules International Journal of Mathematics and Mathematical Sciences |
| title | δ-Small Submodules and δ-Supplemented Modules |
| title_full | δ-Small Submodules and δ-Supplemented Modules |
| title_fullStr | δ-Small Submodules and δ-Supplemented Modules |
| title_full_unstemmed | δ-Small Submodules and δ-Supplemented Modules |
| title_short | δ-Small Submodules and δ-Supplemented Modules |
| title_sort | δ small submodules and δ supplemented modules |
| url | http://dx.doi.org/10.1155/2007/58132 |
| work_keys_str_mv | AT yongduowang dsmallsubmodulesanddsupplementedmodules |