Abstract: Let R be an ideal of a ring with unity, M_R be a R-module. Then M also can be viewed as a I-module. It is proved that some elementary properties of the theory of modules, such as purity, pure-injectivity, elementary equivalent, elementary embedding etc. are reserved between M_R and M_I.

Key words: model theory, theory of modules, elementary properties

摘要： 设I是有单位元的环R的一个理想，M_R是一个R-模，则M_R也可看作一个I-模M_I。证明了M_R与M_I之间，模理论的纯性、纯入射性、初等等价、初等嵌入等初等性质都是保持的。

关键词: 模型论, 模理论, 初等性质