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 ${\mathcal{F}\mathcal{P}}_n(R)$ the full subcategory of $R$-Mod of finitely $n$-presented modules. We prove that ${\mathcal{F}\mathcal{P}}_n(R)$ is an exact category, $K_i(R)=K_i({\mathcal{F}\mathcal{P}}_n(R))$ for every $i\ge 0$ and obtain an expression of ${\mathrm{Nil}}_i(R)$.

11 pages, minor changes