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arXiv · 2409.08334

Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules

Viviana Gubitosi·Rafael Parra
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Abstract

Let $R$ be a ring. In \cite{MD4} Mao and Ding defined an special class of $R$-modules that they called \( FP_n \)-projective $R$-modules. In this paper, we give some new characterizations of \( FP_n \)-projective $R$-modules and strong $n$-coherent rings. Some known results are extended and some new characterizations of the \( FP_n \)-injective global dimension in terms of \( FP_n \)-projective $R$-modules are obtained. Using the \( FP_n \)-projective dimension of an $R$-module defined by Ouyang, Duan and Li in \cite{Ouy} we introduce a slightly different \( FP_n \)-projective global dimension over the ring $R$ which measures how far away the ring is from being Noetherian. This dimension agrees with the $(n,0)$-projective global dimension of \cite{Ouy} when the ring in question is strong $n$-coherent.

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Viviana Gubitosi, Rafael Parra. 2024-09-12. Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules. https://arxiv.org/abs/2409.08334

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