When are the rings $I:I$ Gorenstein?

Abstract

Let $I(\ne A)$ be an ideal of a $d$-dimensional Noetherian local ring $A$ with ${\mathrm{ht}}_{A}I\ge 2$, containing a non-zerodivisor. The problem of when the ring $I:I={\mathrm{End}}_{A}I$ is Gorenstein is studied, in connection with the problem of the Gorensteinness in Rees algebras ${\mathcal{R}}_A(Q^d)$ for certain parameter ideals $Q$ of $A$, that was closely explored by the preceding paper of the second and third authors. Examples are given.

16 pages

References in corpus (1)

• Self-injective commutative rings have no nontrivial rigid ideals