Semi-Modules Which are E-Piequvelent to Projective Semi-Module

Abstract

The aim of this study is an expanded study of the concept projective semi module. I projective property was defined for the module in a certain way, and we described it for the semi-module as follows: a semi-module X is projective if for any surjective hom f  and any hom , a hom h: X   s.t f h(X)   g(X). This concept is closed, as in modules, under direct sum. X is an E-piequvelent semi-module to Y if there are surjective homs h: X   and g: Y . Any semi-module is a projective semi-module if and only if it is an im-projective semi-module and quasi-projective semi-module, where a semi-module M is quasi-projective if, for any surjective hom , and any  g:M , ∃a hom   s.t f = .