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arXiv · 2510.02698

Ulrich modules over local rings of dimension two

Srikanth B. Iyengar·Linquan Ma·Mark E. Walker
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Abstract

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.

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Srikanth B. Iyengar, Linquan Ma, Mark E. Walker. 2025-10-03. Ulrich modules over local rings of dimension two. https://arxiv.org/abs/2510.02698

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