Stable ideals in Gorenstein local rings (Q757501)

It has been shown by \textit{G. Valla} [J. Algebra 58, 247-250 (1979; Zbl 0428.13010)] that for a Cohen-Macaulay local ring (R,m) and an m-primary ideal I the associated graded ring \(G(I)=\oplus_{n\geq 0}I^ n/I^{n+1} \) is Cohen-Macaulay when I is stable, i.e. \(I^ 2=IJ\) for some parameter ideal \(J\subseteq I\). In this note the author investigates the replacement of Cohen-Macaulay by Gorenstein. The main result states that, for R Gorenstein and I stable, G(I) is Gorenstein if and only if, either I is a parameter ideal, or the multiplicity of I is \(2\times length(R/I)\). Using this criterion the author produces many examples of (R,I) with I stable such G(I) is Gorenstein, especially for small dim(R).