Generalizations of Hopfian and co-Hopfian modules

Yongduo Wang

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-6

Abstract:

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:715470

DOI: 10.1155/IJMMS.2005.1455

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