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(m,n)-Cotorson modules and (m,n)-flat modules
- WANG Xi, SHEN Lei, LUO Xiao-qiang
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JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):
10-17.
doi:10.6040/j.issn.1671-9352.0.2020.429
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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. Whats more, R is said to (m,n)-perfectring if all R-modules are (m,n)-cotorsion. Some properties are given.