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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| Format: | Article |
| Language: | English |
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Hindawi Limited
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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doaj-ce0a06b4ead541dab0b90ae2ff2668cb2020-11-24T21:04:25ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yongduo Wang Nanqing Ding |
| spellingShingle |
Yongduo Wang Nanqing Ding Generalized lifting modules International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Yongduo Wang Nanqing Ding |
| author_sort |
Yongduo Wang |
| title |
Generalized lifting modules |
| title_short |
Generalized lifting modules |
| title_full |
Generalized lifting modules |
| title_fullStr |
Generalized lifting modules |
| title_full_unstemmed |
Generalized lifting modules |
| title_sort |
generalized lifting modules |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2006-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/IJMMS/2006/47390 |
| work_keys_str_mv |
AT yongduowang generalizedliftingmodules AT nanqingding generalizedliftingmodules |
| _version_ |
1716771168716849152 |