Acta Scientiarum Naturalium Universitatis Pekinensis

Previous Articles     Next Articles

Preservation of Elementary Properties of the Theory of Modules when Their Underlying Ring is Limited to an Ideal of the Ring

WANG Hanpin   

  1. Department of Computer Science and Technology, Peking University, Beijing, 100871
  • Received:1996-02-05 Online:1997-01-20 Published:1997-01-20



  1. 北京大学计算机科学和技术系,北京,100871

Abstract: Let R be an ideal of a ring with unity, MR 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 MR and MI.

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

摘要: I是有单位元的环R的一个理想,MR是一个R-模,则MR也可看作一个I-模MI。证明了MRMI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

CLC Number: