兰州理工大学学报

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (4): 154-156.

• 数理科学 • 上一篇    下一篇

D4-δ-盖及其应用

王永铎, 王亚婷   

  1. 兰州理工大学 理学院, 甘肃 兰州 730050
  • 收稿日期:2018-07-12 出版日期:2020-08-28 发布日期:2020-11-10
  • 作者简介:王永铎(1974-),男,甘肃靖远人,博士,教授.
  • 基金资助:
    国家自然科学基金(11861043)

D4-δ-covers and their applications

WANG Yong-duo, WANG Ya-ting   

  1. School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China
  • Received:2018-07-12 Online:2020-08-28 Published:2020-11-10

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摘要： 引入了D4-δ-盖的概念,即称(F,g)为模M的D4-δ-盖,若F是D4-模,g是F到M的满同态,且Ker(g)《δF.研究了D4-δ-盖的性质以及它与投射δ-盖之间的联系,并用D4-δ-盖刻画了δ-完备环(半完备环,半正则环).

关键词: D4-δ-盖, δ-完备环, δ-半完备环, δ-半正则环

Abstract: The concept of D4-δ-covers is introduced. A pair (F,g) is called a D4-δ-cover of a module M if F is a D4-δ-module, g an epimorphism of F onto M, and Ker(g)《δF. The properties of D4-δ-cover and their relations to projective δ-cover are studied and δ-perfect rings (semiperfect rings, semiregular rings) are characterized by using D4-δ-covers.

Key words: D4-δ-cover, δ-perfect ring, δ-semiperfect ring, δ-semiregular ring

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