On semi-projective modules and their endomorphism rings

Abstract

This paper provides the several homological characterization of perfect rings and semi-simple rings in terms of semi-projective modules. We investigate whether Hopkins-Levitzki Theorem extend to semi-projective module i.e. whether there exists an artinian semi-projective module which are noetherian. Unfortunately, the answer we have is negative; counter example is given. However, it is shown that the answer is positive for certain large classes of semi-projective modules in Proposition 2.26. We have discussed the summand intersection property, summand sum property for semi-projective modules. Apart from this, we have introduced the idea of M-hollow modules, also several necessary and sufficient conditions are established when the endomorphism rings of a semi-projective modules is a local ring. © 2018 World Scientific Publishing Company.