限制到理想时模理论的初等性质的保持性

北京大学学报（自然科学版）

限制到理想时模理论的初等性质的保持性

王捍贫

北京大学计算机科学和技术系，北京，100871

收稿日期:1996-02-05 出版日期:1997-01-20 发布日期:1997-01-20

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

WANG Hanpin

Department of Computer Science and Technology, Peking University, Beijing, 100871

Received:1996-02-05 Online:1997-01-20 Published:1997-01-20

摘要/Abstract

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

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

中图分类号:

O141.4

王捍贫. 限制到理想时模理论的初等性质的保持性[J]. 北京大学学报（自然科学版）.

WANG Hanpin . Preservation of Elementary Properties of the Theory of Modules when Their Underlying Ring is Limited to an Ideal of the Ring[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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链接本文: https://xbna.pku.edu.cn/CN/

https://xbna.pku.edu.cn/CN/Y1997/V33/I1/104

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[2]	王捍贫, 谢惠扬. L(Q)格值模型的省略型定理[J]. 北京大学学报（自然科学版）, 1999, 35(3): 409-413.
[3]	王捍贫 . 分式化时模的模型论性质的保持性[J]. 北京大学学报（自然科学版）, 1997, 33(3): 368-374.