Generalized lifting modules
We introduce the concepts of lifting modules and (quasi-)discrete modules relative to a given left module. We also introduce the notion of SSRS-modules. It is shown that (1) if M is an amply supplemented module and 0→N′→N→N″→0 an exact sequence, then M is N-lifting if and only if it is N′-lifting...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/47390 |
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| _version_ | 1850175477010923520 |
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| author | Yongduo Wang Nanqing Ding |
| author_facet | Yongduo Wang Nanqing Ding |
| author_sort | Yongduo Wang |
| collection | DOAJ |
| description | We introduce the concepts of lifting modules and (quasi-)discrete
modules relative to a given left module. We also introduce the
notion of SSRS-modules. It is shown that (1) if M
is
an amply supplemented module and 0→N′→N→N″→0
an exact sequence, then M is
N-lifting if and only if it is N′-lifting and N″-lifting;
(2) if M is a Noetherian module, then M is lifting if and only
if M is R-lifting if and only if M is an amply supplemented
SSRS-module; and (3) let M be an amply supplemented SSRS-module
such that Rad(M) is finitely generated, then M=K⊕K′,
where K
is a radical module and K′
is a lifting module. |
| format | Article |
| id | doaj-art-ce0a06b4ead541dab0b90ae2ff2668cb |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ce0a06b4ead541dab0b90ae2ff2668cb2025-08-20T02:19:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/4739047390Generalized lifting modulesYongduo Wang0Nanqing Ding1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Mathematics, Nanjing University, Nanjing 210093, ChinaWe introduce the concepts of lifting modules and (quasi-)discrete modules relative to a given left module. We also introduce the notion of SSRS-modules. It is shown that (1) if M is an amply supplemented module and 0→N′→N→N″→0 an exact sequence, then M is N-lifting if and only if it is N′-lifting and N″-lifting; (2) if M is a Noetherian module, then M is lifting if and only if M is R-lifting if and only if M is an amply supplemented SSRS-module; and (3) let M be an amply supplemented SSRS-module such that Rad(M) is finitely generated, then M=K⊕K′, where K is a radical module and K′ is a lifting module.http://dx.doi.org/10.1155/IJMMS/2006/47390 |
| spellingShingle | Yongduo Wang Nanqing Ding Generalized lifting modules International Journal of Mathematics and Mathematical Sciences |
| title | Generalized lifting modules |
| title_full | Generalized lifting modules |
| title_fullStr | Generalized lifting modules |
| title_full_unstemmed | Generalized lifting modules |
| title_short | Generalized lifting modules |
| title_sort | generalized lifting modules |
| url | http://dx.doi.org/10.1155/IJMMS/2006/47390 |
| work_keys_str_mv | AT yongduowang generalizedliftingmodules AT nanqingding generalizedliftingmodules |