$q$-Krull dimension of commutative rings
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909169641062400 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | In this paper, we introduce and study the $q$-Krull dimension of a commutative ring via its $q$-operation. A new characterization of $τ_q$-von Neumann regular rings is obtained, and some properties of rings $q$-Krull dimension 0 are studied. Moreover, we characterize the $q$-Krull dimension of $τ_q$-Noetherian rings in terms of Krull dimension of some total quotient rings. Besides, we show that every ring with $w$-Krull dimension $0$ is a \DW\ ring, positively answers an question proposed by H. Kim. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-Krull dimension of commutative rings Zhang, Xiaolei Commutative Algebra In this paper, we introduce and study the $q$-Krull dimension of a commutative ring via its $q$-operation. A new characterization of $τ_q$-von Neumann regular rings is obtained, and some properties of rings $q$-Krull dimension 0 are studied. Moreover, we characterize the $q$-Krull dimension of $τ_q$-Noetherian rings in terms of Krull dimension of some total quotient rings. Besides, we show that every ring with $w$-Krull dimension $0$ is a \DW\ ring, positively answers an question proposed by H. Kim. |
| title | $q$-Krull dimension of commutative rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.09429 |