The small finitistic dimensions of commutative rings, II
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929497784188928 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | The small finitistic dimension $\fPD(R)$ of a ring $R$ is defined to be the supremum of projective dimensions of $R$-modules with finite projective resolutions. In this paper, we investigate the small finitistic dimensions of four types of ring constructions: polynomial rings, formal power series rings, trivial extensions and amalgamations. Besides, we show the small finitistic dimensions of a ring is less than or equal to its Krull dimension. We also give a total ring of quotients with infinite small finitistic dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The small finitistic dimensions of commutative rings, II Zhang, Xiaolei Commutative Algebra The small finitistic dimension $\fPD(R)$ of a ring $R$ is defined to be the supremum of projective dimensions of $R$-modules with finite projective resolutions. In this paper, we investigate the small finitistic dimensions of four types of ring constructions: polynomial rings, formal power series rings, trivial extensions and amalgamations. Besides, we show the small finitistic dimensions of a ring is less than or equal to its Krull dimension. We also give a total ring of quotients with infinite small finitistic dimension. |
| title | The small finitistic dimensions of commutative rings, II |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.13394 |