Rings with nonzero maps between non-projective modules

Abstract

In this paper, we characterize rings admitting nonzero homomorphisms between nonzero modules. Also, we characterize rings satisfying the following property: There exists a nonzero homomorphism between any two non-projective modules.

Keywords:

• Non-zero homorphism
• projective module
• ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16D10; 16D50
• Secondary: 16P20

Acknowledgments

The author would like to thank the referee for careful checking of the details and helpful comments that improved this paper.