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 |