Ulrich ideals and almost Gorenstein rings

Goto, Shiro; Takahashi, Ryo; Taniguchi, Naoki

doi:10.1090/proc/12970

Ulrich ideals and almost Gorenstein rings
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Proc. Amer. Math. Soc. 144 (2016), 2811-2823 Request permission

Abstract:

The structure of the complex $\mathrm {\textbf {R}Hom}_R(R/I,R)$ 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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