On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective
نویسنده
چکیده مقاله:
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.
منابع مشابه
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 m...
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عنوان ژورنال
دوره 4 شماره 2
صفحات 19- 29
تاریخ انتشار 2016-12-01
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