Notes on Generalized Hopfian and Weakly Co-Hopfian Modules

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.

Key Words:

• Generalized Hopfian modules
• Generalized Hopfian rings
• Matrix rings
• Truncated polynomial rings
• Weakly co-Hopfian modules

2000 Mathematics Subject Classification:

• 16D10
• 16P40

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.