Let R be a Cohen-Macaulay local K-algebra or a standard graded K-algebra over a field K with a canonical module omega(R). The trace of omega(R) is the ideal tr(omega(R)) of R which is the sum of those ideals phi(omega(R)) with phi is an element of Hom(R) (omega(R),R- ) . The smallest number s for which there exist phi(1),...,phi(s) is an element of Hom(R) (omega(R),R- ) with tr(omega(R)) = phi(1)(omega(R)) + ... + phi(s) (omega(R)) is called the Teter number of R. We say that R is of Teter type if s = 1. It is shown that R is not of Teter type if R is generically Gorenstein. In the present paper, we focus especially on zero-dimensional graded and monomial K-algebras and present various classes of such algebras which are of Teter type.