Abstract: | Erika Mares introduced the concepts of semi-perfectness and perfectness for projective modules, generalised the structure theorems of H. Bass and obtained results on the endomorphism rings of such modules. The present author has carried out an extensive study of endomorphism rings of various types of modules with two of his collaborators [3], [9]. In particular the concept of semi-perfectness was extended to modules not necessarily projective and results similar to those of Erika Mares obtained for quasi-projective semi-perfect modules. The object of the present paper is to extend the concept of perfectness to modules which are not necessarily projective and obtain results similar to those of Erika Mares, Roger Ware etc. concerning these modules. |