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arXiv · 1507.04556

Ulrich ideals and almost Gorenstein rings

Shiro Goto·Ryo Takahashi·Naoki Taniguchi
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Abstract

The structure of the complex $\operatorname{\mathbf{R}Hom}_R(R/I,R)$ is explored for an Ulrich ideal $I$ in a Cohen-Macaulay local ring $R$. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.

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Shiro Goto, Ryo Takahashi, Naoki Taniguchi. 2015-07-16. Ulrich ideals and almost Gorenstein rings. https://arxiv.org/abs/1507.04556

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