  Let R be a Cohen-Macaulay local ring possessing a canonical module. In this
paper we consider when the maximal ideal of R is self-dual, i.e. it is
isomorphic to its canonical dual as an R-module. local rings satisfying this
condition are called Teter rings, and studied by Teter, Huneke-Vraciu,
Ananthnarayan-Avramov-Moore, and so on. On the positive dimensional case, we
show such rings are exactly the endomorphism rings of the maximal ideals of
some Gorenstein local rings of dimension one. We also provide some connection
between the self-duality of the maximal ideal and near Gorensteinness.
