Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914420719878144 |
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| author | Gubitosi, Viviana Parra, Rafael |
| author_facet | Gubitosi, Viviana Parra, Rafael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules Gubitosi, Viviana Parra, Rafael Rings and Algebras 16D10, 16D40, 16D50, 16E60 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. |
| title | Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules |
| topic | Rings and Algebras 16D10, 16D40, 16D50, 16E60 |
| url | https://arxiv.org/abs/2409.08334 |