When are the rings $I:I$ Gorenstein?

Abstract

Let I ( = A) be an ideal of a d-dimensional Noetherian local ring A with ht A I ≥ 2, containing a non-zerodivisor. The problem of when the ring I : I = End A I is Gorenstein is studied, in connection with the problem of the Gorensteinness in Rees algebras R A (Q d ) for certain parameter ideals Q of A, that was closely explored by the preceding paper [8] of the authors. Examples are given.