on two generalizations of semi-projective modules: sgq-projective and $pi$-semi-projective

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a module $m$ is called an sgq-projective module if for any $phiin s$, there exists a right ideal $x_phi$ of $s$ such that $d_s(im phi)=phi soplus x_phi$ as right $s$-modules. we call $m$ a $pi$-semi-projective module if for any $0neq sin s$, there exists a positive integer $n$ such that $s^nneq 0$ and any $r$-homomorphism from $m$ to $s^nm$ can be extended to an endomorphism of $m$. some properties of this class of modules are investigated.