Envelopes and Covers by Modules of Finite FP-Injective and Flat Dimensions

Let R be a ring, n a fixed non-negative integer and ℱ ℐ n (ℱ n ) the class of all right (left) R-modules of FP-injective (flat) dimension at most n. We prove that ( is a perfect cotorsion theory if R is a right coherent ring with FP-id(R R ) ≤ n. This result was proven by Aldrich, Enochs, Jenda, and Oyonarte in Noetherian case. The modules in are also studied. Some applications are given.

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