ABSTRACT
1. Definitions. 2. Infective factor and projective submodules. 3. Semi-hereditary modules. 4. Characterization. 5. M semihereditary in σ[M]. 6. He-reditary modules. 7. Properties. 8. Mhereditary in σ[M]. 9. Locally noethe-rian hereditary modules. 10. Left PP-endomorphism rings. 11. Right PP-endomorphism rings. 12. Modules with Sat submodules. 13. Left semihereditary rings. 14. End(M) with semihereditary M. 15.M hereditary in σ[M]. 16. Left hereditary rings. 17. Exercises.
