Abstract
Let R be a ring, M a right R-module, and n a fixed non-negative integer. M is called n-cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R-module N. We prove that (ℱ n , 𝒞 n ) is a complete hereditary cotorsion theory, where ℱ n (resp. 𝒞 n ) denotes the class of all n-flat (resp. n-cotorsion) right R-modules. Several applications are given.
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