数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (2): 391-401.doi: 10.1016/S0252-9602(09)60038-2

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S-SUPERFLUOUS AND S-ESSENTIAL HOMOMORPHISMS

朱海燕,丁南庆   

  1. Department of Mathematics, Zhejiang University of Technology, Zhejiang 310023, China
  • 收稿日期:2006-11-08 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:

    Supported by Specialized Research Fund for the Doctoral Program of Higher Education (20050284015) and National Natural Science Foundation of China (10771096)

S-SUPERFLUOUS AND S-ESSENTIAL HOMOMORPHISMS

Zhu Haiyan, Ding Nanqing   

  1. Department of Mathematics, Zhejiang University of Technology, Zhejiang 310023, China
  • Received:2006-11-08 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    Supported by Specialized Research Fund for the Doctoral Program of Higher Education (20050284015) and National Natural Science Foundation of China (10771096)

摘要:

Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As appli-cations, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.

关键词: S-essential, monomorphism, S-superfluous, epimorphism, (pre)cover,  (pre)envelope

Abstract:

Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As appli-cations, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.

Key words: S-essential, monomorphism, S-superfluous, epimorphism, (pre)cover,  (pre)envelope

中图分类号: 

  • 16D10