International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 507-512
Epis and monos which must be isos
Department of Mathematics and Statistics, University of Guelph, Guelph N1G 2W1, Ontario, Canada
Received 21 March 1984
Copyright © 1984 David J. Fieldhouse. 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.
Orzech  has shown that every surjective endomorphism of a noetherian module is an isomorphism. Here we prove analogous results for injective endomorphisms of noetherian injective modules, and the duals of these results. We prove that every injective endomorphism, with large image, of a module with the descending chain condition on large submodules is an isomorphism, which dualizes a result of Varadarajan . Finally we prove
the following result and its dual: if is any radical then every surjective endomorphism of a module , with kernel contained in , is an isomorphism, provided that every surjective endomorphism of is an isomorphism.