Local rings with self-dual maximal ideal (Q2192225)

Let \(R\) be a Cohen-Macaulay ring possessing a canonical module. Then \(R\) is called a \textit{Teter ring} if \(R\) is non-Gorenstein and \(R\cong S/\mathrm{soc}(S)\) for some Artinian Gorenstein ring \(S.\) The goal of the paper is to study the one-dimensional Teter rings. It is shown that in this case Teter rings coincide with the endomorphism rings of the maximal ideal of some one-dimensional Gorenstein local rings. Several other characterizations of one-dimensional Teter rings are given. Several applications are given, e.g. a characterization of the endomorphism ring of a local hypersurface of dimension one. Examples and questions are mentioned.