Generalizations of Hopfian and co-Hopfian modules
Let R be a ring and M a left R-module. M which satisfies DCC on essential submodules is GCH, and M which satisfies ACC on small submodules is WH. If M[X] is GCH R[X]-module, then M is GCH R-module. Examples show that a GCH module need not be co-Hopfian and a WH module need not be Hopfian.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1455 |
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doaj-f999f972a3514988a62b8981b13056912020-11-24T22:08:03ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200591455146010.1155/IJMMS.2005.1455Generalizations of Hopfian and co-Hopfian modulesYongduo Wang0Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaLet R be a ring and M a left R-module. M which satisfies DCC on essential submodules is GCH, and M which satisfies ACC on small submodules is WH. If M[X] is GCH R[X]-module, then M is GCH R-module. Examples show that a GCH module need not be co-Hopfian and a WH module need not be Hopfian.http://dx.doi.org/10.1155/IJMMS.2005.1455 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yongduo Wang |
| spellingShingle |
Yongduo Wang Generalizations of Hopfian and co-Hopfian modules International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Yongduo Wang |
| author_sort |
Yongduo Wang |
| title |
Generalizations of Hopfian and co-Hopfian modules |
| title_short |
Generalizations of Hopfian and co-Hopfian modules |
| title_full |
Generalizations of Hopfian and co-Hopfian modules |
| title_fullStr |
Generalizations of Hopfian and co-Hopfian modules |
| title_full_unstemmed |
Generalizations of Hopfian and co-Hopfian modules |
| title_sort |
generalizations of hopfian and co-hopfian modules |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| description |
Let R be a ring and M a left R-module. M which satisfies
DCC on essential submodules is GCH, and M which satisfies ACC on
small submodules is WH. If M[X] is GCH R[X]-module, then M is GCH R-module. Examples show that a GCH module need not be
co-Hopfian and a WH module need not be Hopfian. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.1455 |
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AT yongduowang generalizationsofhopfianandcohopfianmodules |
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1725817901553811456 |