Let R be a strong n-coherent ring such that each finitely n-presented R-module has finite projective dimension. We consider ℱ?n(R) the full subcategory of R-Mod of finitely n-presented modules. We prove that ℱ?n(R) is an exact category, Ki(R)=Ki(ℱ?n(R)) for every i≥0 and we obtain an expression of Nili(R).
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