On $\Pi$-coherence of rings

Abstract

Let $n$ be a fixed positive integer. A ring $R$ is called left $n$-$\Pi$-coherent if every $n$-generated torsionless left $R$-module is finitely presented, some characterizations and applications of $n$-$\Pi$-coherent rings are obtained.

Keywords

• n-$\Pi$-coherent rings,n-GF rings,n-semihereditary rings,strongly n-semihereditary rings

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