JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (1): 10-17.doi: 10.6040/j.issn.1671-9352.0.2020.429

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(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

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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

CLC Number: 

  • O154
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