
(m,n)Cotorson modules and (m,n)flat modules
 WANG Xi, SHEN Lei, LUO Xiaoqiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):
1017.
doi:10.6040/j.issn.16719352.0.2020.429

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Let R be a ring, m and n be two fixed nonnegative integers. A right Rmodule C is called (m,n)cotorsion if Ext^{m+1}_{R}(N,C)=0 for any right Rmodule with fd_{}RN≤n. M is called (m,n)flat if Ext^{1}_{}R(M,C)=0 for any (m,n)cotorsion right Rmodules C. We prove that(F ^{m}_{n},C ^{m}_{n} )is a complete hereditary cotorsion pair, where F ^{m}_{n}, C ^{m}_{n} denotes the class of all (m,n)flat and (m,n)cotorsion right Rmodules respectively. Whats more, R is said to (m,n)perfectring if all Rmodules are (m,n)cotorsion. Some properties are given.