We introduce the notion of semi-poor modules and consider the possibility that all modules are either injective or semi-poor. This notion gives a generalization of poor modules that have minimal injectivity domain. A module $M$ is called semi-poor if whenever it is $N$-injective and $N\ne 0$, then the module $N$ has nonzero socle. In this paper the properties of semi-poor modules are investigated and are used to characterize various families of rings. We introduce the rings over which every module is either semi-poor or injective and call such condition property $(P)$. The structure of the rings that have the property $(P)$ is completely determined. Also, we give some characterizations of rings with the property $(P)$ in the language of the lattice of hereditary pretorsion classes over a given ring. It is proved that a ring $R$ has the property $(P)$ iff either $R$ is right semi-Artinian or $R=R_1\times R_2$ where $R_1$ is a semisimple Artinian ring and $R_2$ is right strongly prime and a right $c$-ring with zero right socle.

我们引入了半穷模块的概念，并考虑了所有模块都是单射或半穷的可能性。这个概念给出了具有最小注入域的不良模块的概括。一个模块$米$被称为半穷人，如果它是$ñ$-内射和$ñ\ne 0$, 那么模块$ñ$具有非零坐标。在本文中，研究了半贫模的性质，并用于表征各种环族。我们引入了每个模块是半穷或单射的环，并将这种条件属性称为$(磷)$. 具有属性的环的结构$(磷)$是完全确定的。此外，我们给出了环的一些特征$(磷)$用给定环上的遗传预扭转等级格的语言。证明了一个环$R$有财产$(磷)$当且仅当$R$是右半阿蒂尼安或$R=R_1\times R_2$在哪里$R_1$是一个半单阿蒂尼环，并且$R_2$是正确的强素数和正确的$C$- 右脚为零的环。