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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (1): 10-17.doi: 10.6040/j.issn.1671-9352.0.2020.429

• • 上一篇    

(m,n)-余挠模与(m,n)-平坦模

王茜1,沈磊2,罗肖强1   

  1. 1.四川文理学院数学学院, 四川 达州 635000;2.南京大学数学系, 江苏 南京 210093
  • 发布日期:2021-01-05
  • 作者简介:王茜(1990— ), 女, 硕士, 助教, 研究方向为同调代数. E-mail:xwang1233@163.com
  • 基金资助:
    四川文理学院科研启动专项(2019KZ007Z);四川文理学院创新团队基金(2018KC0012)

(m,n)-Cotorson modules and (m,n)-flat modules

WANG Xi1, SHEN Lei2, LUO Xiao-qiang1   

  1. 1. College of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, Sichuan, China;
    2. Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu, China
  • Published:2021-01-05

摘要: 设R是环,m,n是非负整数,称右R-模C是(m,n)-余挠模,是指对任何平坦维数不超过n的右R-模N,都有Extm+1R(N,C)=0。称右R-模M为(m,n)-平坦模,是指对任何(m,n)-余挠模C,都有Ext1R(M,C)=0。证明了(F mn,C mn〓)是完备的遗传余挠对,其中F mn,C mn〓分别表示(m,n)-平坦模类与(m,n)-余挠模类。此外,称环R是(m,n)-完全环,是指所有R-模都是(m,n)-余挠模的环。给出了(m,n)-完全环的一些刻画。

关键词: (m,n)-余挠模, (m,n)-平坦模, (m,n)-完全环

Abstract: Let R be a ring, m and n be two fixed non-negative integers. A right R-module C is called (m,n)-cotorsion if Extm+1R(N,C)=0 for any right R-module with fdRN≤n. M is called (m,n)-flat if Ext1R(M,C)=0 for any (m,n)-cotorsion right R-modules C. We prove that(F mn,C mn )is a complete hereditary cotorsion pair, where F mn, C mn denotes the class of all (m,n)-flat and (m,n)-cotorsion right R-modules respectively. Whats more, R is said to (m,n)-perfectring if all R-modules are (m,n)-cotorsion. Some properties are given.

Key words: (m,n)-cotorsion module, (m,n)-flat module, (m,n)-perfect ring

中图分类号: 

  • O154
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