Ulrich ideals and almost Gorenstein rings
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2015
- DOI:
- 10.48550/arXiv.1507.04556
- arXiv:
- arXiv:1507.04556
- Bibcode:
- 2015arXiv150704556G
- Keywords:
-
- Mathematics - Commutative Algebra;
- 13H10;
- 13H15;
- 13D07
- E-Print:
- 13 pages