Let R be an associative ring with identity,m and n be fixed positive integers.The notions of(m,n)-injective functors and(m,n)-flat functors are introduced.Some properties of these two classes of functors are studied and some equivalent characterizations for(m,n)-coherent rings and Von Neumann regular rings are given in terms of(m,n)-injective functors and(m,n)-flat functors.
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