Good ideals in Gorenstein local rings obtained by idealization (Q2758967)

Let \(A\) be a Gorenstein local ring. An ideal \(I \subset A\) of height \(s\) is said to be good if \(I\) contains a reduction generated by \(s\) elements and the associated graded ring of \(I\) is Gorenstein of a-invariant \(-s+1\). Goto and Kim showed that almost all Gorenstein local rings have infinitely many good ideals in the preceding paper. In the present paper, the authors concentrated on a special Gorenstein local ring. If \(R\) is a Cohen-Macaulay local ring with canonical module \(K_R\), then the idealization \(R \ltimes K_R\) is a Gorenstein local ring. The authors characterize all good ideals in such a Gorenstein ring.