Abstract Quasi-Frobenius rings are precisely rings over which any right module is a homomorphic image of an injective module. We investigate the structure of rings whose proper cyclic right modules are homomorphic image of injectives. The class of such rings properly contains that of right self-injective rings. We obtain some structure theorems for rings satisfying the said property and apply them to the Artin algebra case: It follows that an Artin algebra with this property is Quasi-Frobenius.

中文翻译：

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当适当的循环是单射的同态图像时

摘要 拟 Frobenius 环是精确的环，在该环上任何正确的模块都是单射模块的同态图像。我们研究了环的结构，其适当的循环右模块是单射的同态图像。这种环的类正确地包含正确的自注入环的类。我们获得了满足上述性质的环的一些结构定理，并将它们应用到 Artin 代数的情况： 具有这个性质的 Artin 代数是拟 Frobenius。