Abstract
In this article, the generalized Hopficity and weakly co-Hopficity of modules over truncated polynomial and triangular matrix rings are considered. Also, it is obtained partially when the direct product R × S is a generalized Hopfian ring, where R and S are two rings.
ACKNOWLEDGMENTS
This work was partially supported by the National Science Foundation of China (No. 10961021, 10901129) and a grant from Lanzhou Jiaotong University (No. 409039). The authors would like to thank the referee for valuable suggestions and comments, which improved the present article. Especially, the referee provided a correct proof of Lemma 2.1.
Notes
Communicated by A. Toma.