Abstract:

The authors presented  the concepts of  co-projective modules and  co-injective modules related to the hereditary torsion theory and proved some equivalent conditions of these two types of modules,  revealed the duality of these two types of modules,  gave the concepts of co-semisimple rings and left co-hereditary rings by means of co-projective module related to the hereditary torsion theory and studied the structure of these two types of rings.

Key words: τcoinjective module, τcoprojective module, τtorsionmodule, τtorsion free module