K-theory of n-coherent rings

Abstract

Let $R$ be a strong $n$-coherent ring such that each finitely $n$-presented $R$-module has finite projective dimension. We consider $\mathcal{FP}_{n}(R)$ the full subcategory of $R$-Mod of finitely $n$-presented modules. We prove that $\mathcal{FP}_{n}(R)$ is an exact category, $K_{i}(R) = K_{i}(\mathcal{FP}_{n}(R))$ for every $i\geq 0$ and obtain an expression of $\operatorname{Nil}_{i}(R)$.