$(n,d)$-Coherent Rings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914494084546560 |
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| author | Parra, Rafael |
| author_facet | Parra, Rafael |
| contents | We investigate finiteness conditions on modules of bounded projective dimension and their connection with generalized notions of coherence. For a ring $R$, we consider the class $\mathsf{FP}_n^{\le d}(R)$ of finitely $n$-presented modules of projective dimension at most $d$ and develop the corresponding relative homological theory. We establish several characterizations of left $(n,d)$-coherent rings in the sense of Mao and Ding [43], in terms of $\mathsf{FP}_n^{\le d}(R)$ and the associated classes of $\mathsf{FP}_n^{\le d}$-injective, $\mathsf{FP}_n^{\le d}$-projective, $\mathsf{FP}_n^{\le d}$-flat, and $\mathsf{FP}_n^{\le d}$-cotorsion modules. As a consequence, when $d \ge \gD(R)$ or $d=\infty$, we recover Costa's $n$-coherence [17] and obtain new characterizations of regularly coherent rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $(n,d)$-Coherent Rings Parra, Rafael Rings and Algebras We investigate finiteness conditions on modules of bounded projective dimension and their connection with generalized notions of coherence. For a ring $R$, we consider the class $\mathsf{FP}_n^{\le d}(R)$ of finitely $n$-presented modules of projective dimension at most $d$ and develop the corresponding relative homological theory. We establish several characterizations of left $(n,d)$-coherent rings in the sense of Mao and Ding [43], in terms of $\mathsf{FP}_n^{\le d}(R)$ and the associated classes of $\mathsf{FP}_n^{\le d}$-injective, $\mathsf{FP}_n^{\le d}$-projective, $\mathsf{FP}_n^{\le d}$-flat, and $\mathsf{FP}_n^{\le d}$-cotorsion modules. As a consequence, when $d \ge \gD(R)$ or $d=\infty$, we recover Costa's $n$-coherence [17] and obtain new characterizations of regularly coherent rings. |
| title | $(n,d)$-Coherent Rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2603.25679 |