Ulrich ideals and almost Gorenstein rings

Abstract

The structure of the complex R H o m R ( R / I , R ) \mathrm {\textbf {R}Hom}_R(R/I,R) is explored for an Ulrich ideal I I in a Cohen–Macaulay local ring R 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.