广西师范大学学报（哲学社会科学版） ›› 2021, Vol. 39 ›› Issue (2): 119-124.doi: 10.16088/j.issn.1001-6600.2019082802

• CCIR2020 • 上一篇    下一篇

φ-平坦余挠理论

张晓磊1*, 赵伟2, 王芳贵1   

  1. 1.四川师范大学 数学科学学院, 四川 成都 610068;
    2.阿坝师范学院 数学与计算机科学学院, 四川 阿坝 623002
  • 收稿日期:2019-08-28 修回日期:2019-11-09 出版日期:2021-03-25 发布日期:2021-04-15
  • 通讯作者: 张晓磊(1986—),男,山东青岛人,四川师范大学博士研究生。E-mail:zxlrghj@163.com
  • 基金资助:
    国家自然科学基金(11671283)

On φ-flat Cotorsion Theory

ZHANG Xiaolei1*, ZHAO Wei2, WANG Fanggui1   

  1. 1. School of Mathematical Sciences, Sichuan Normal University, Chengdu Sichuan 610068, China;
    2. School of Mathematics and Computer Science, Aba Teachers University, Aba Sichuan 623002, China
  • Received:2019-08-28 Revised:2019-11-09 Online:2021-03-25 Published:2021-04-15

摘要： 引进并研究φ-平坦余挠理论, 证明了该余挠理论是完全余挠理论。设R是φ-环, 则φ-平坦余挠理论与经典平坦余挠理论相等当且仅当R是整环。作为应用, 给出了非诣零凝聚环和φ-VN正则环的新刻画和φ-平坦模的包类性质;证明了每个R-模都有一个满的φ-平坦包当且仅当R是非诣零凝聚环,并且φ-平坦模关于子模封闭。

关键词: 余挠理论, 盖类, 包类, φ-平坦模, φ-余挠模

Abstract: In this paper, the φ-flat cotorsion theory which is showed to be a perfect cotorsion theory is introduced and studied. Assume R is a φ-ring. It is proved that the φ-flat cotorsion theory coincides with the classical flat cotorsion theory if and only if R is a domain. As an application, new characterizations of Nonnil-coherent rings and φ-von Neumann rings are given. Finally, the envelope property of φ-flat modules is investigated and showing that every R-module has a surjective (pre)envelope if and only if R is a Nonnil-coherent ring and all φ-flat R-modules are closed under submodules.

Key words: cotorsion theory, covering class, enveloping class, φ-flat module, φ-cotorsion module

中图分类号: 

  • O154.2
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