M-本质内射模和本质内射维数

M-essential Injective Modules and Essential Injective Dimension

在M-内射模的基础上引进了M-本质内射模的概念,研讨了M-本质内射模的一些性质,并且引入了M的本质内射分解和本质内射维数的概念,深入探讨了内射维数和本质内射维数之间的关系,得出了一些重要的结论.

The concept of M-essential injective modules is introduced on the basis of M-injective modules. Some equivalent characterizations of M-essential injective modules are given and the properties of M-essential injective modules are studied. Moreover, some other equivalent characterizations of injective modules and selfinjective rings are given. Similar to the injective resolution of M, the essential injective resolution and left essential injective dimension of M are defined, and the connections between left injective dimension and left essential injective dimension of M are further studied.