Ulrich ideals and almost Gorenstein rings

Abstract

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

13 pages

References in corpus (2)

• Generators and dimensions of derived categories
• The almost Gorenstein Rees algebras over two-dimensional regular local rings

Cited by in corpus (1)

• Almost Gorenstein rings arising from fiber products