Pointwise Projective Modules and Some Related Modules

Abstract

Let R be a commutative ring with 1, and Let M be a (left)R-module. M is said to be pointwise projective if for each epimorphism :A ! B , where A and B are any R modules, and for each homomorphism : M ! B , then for every m 2M , there exists a homomorphism' : M ! A , which may depend on m, such that'(m) = (m). Our mean concern in this paper is to study the relations between pointwise projective modules with cancellation modules and their generalization generator modules, multiplication modules and its generalizations.