RINGS OF TETER TYPE

Abstract

Abstract 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 $\operatorname {tr}(\omega _R)$ of R which is the sum of those ideals $\varphi (\omega _R)$ with ${\varphi \in \operatorname {Hom}_R(\omega _R,R)}$ . The smallest number s for which there exist $\varphi _1, \ldots , \varphi _s \in \operatorname {Hom}_R(\omega _R,R)$ with $\operatorname {tr}(\omega _R)=\varphi _1(\omega _R) + \cdots + \varphi _s(\omega _R)$ 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.