北京大学学报(自然科学版)

分式化时模的模型论性质的保持性

王捍贫   

  1. 北京大学计算机系,北京,100871
  • 收稿日期:1997-01-10 出版日期:1997-05-20 发布日期:1997-05-20

Preservation of Model-theoretic Properties of Modules when It is Fracted

WANG Hanpin   

  1. Department of Computer Science & Technology, Peking University, Beijing, 100871
  • Received:1997-01-10 Online:1997-05-20 Published:1997-05-20

摘要: 将环R的分式环S-1R上的模MS-1R“限制”到R上时,模理论的纯性、纯入射性、初等等价、初等嵌入等模型论性质都是保持的。还讨论了(S-1M)S-1RMR之间模型论性质的保持性。

关键词: 模型论, 模理论, 分式环, 分式模

Abstract: Viewing modules MS-1R over a fractional ring S-1R of a ring R as modules MR over R, It is proved that some model-theoretic properties of modules, such as purity, pure embedding, elementary equivalence, elementary embedding, are preserved. The relations of such properties between MR and (S-1M)S-1R are also considered.

Key words: model theory, theory of modules, fractional ring, fractional module

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