Ulrich modules over local rings of dimension two
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911190610870272 |
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| author | Iyengar, Srikanth B. Ma, Linquan Walker, Mark E. |
| author_facet | Iyengar, Srikanth B. Ma, Linquan Walker, Mark E. |
| contents | It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete intersection domains of dimension two that admit no Ulrich modules. As an application, it is proved that, for this class of rings, the length of a nonzero module of finite projective dimension is at least the multiplicity of the local ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ulrich modules over local rings of dimension two Iyengar, Srikanth B. Ma, Linquan Walker, Mark E. Commutative Algebra 13C13 (primary), 13H10, 13C14, 14F06 (secondary) It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete intersection domains of dimension two that admit no Ulrich modules. As an application, it is proved that, for this class of rings, the length of a nonzero module of finite projective dimension is at least the multiplicity of the local ring. |
| title | Ulrich modules over local rings of dimension two |
| topic | Commutative Algebra 13C13 (primary), 13H10, 13C14, 14F06 (secondary) |
| url | https://arxiv.org/abs/2510.02698 |