International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1455-1460
Generalizations of Hopfian and co-Hopfian modules
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
Received 25 September 2004
Copyright © 2005 Yongduo Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a ring and a left -module. which satisfies
DCC on essential submodules is GCH, and which satisfies ACC on
small submodules is WH. If is GCH -module, then is GCH -module. Examples show that a GCH module need not be
co-Hopfian and a WH module need not be Hopfian.