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RINGS OF TETER TYPE
Published online by Cambridge University Press: 10 June 2022
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.
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- © (2022) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license
Footnotes
Oleksandra Gasanova’s stay was supported by Liljewalchs and Thelins travel scholarships from Uppsala University. Takayuki Hibi was partially supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant No. 19H00637. Somayeh Moradi was supported by the Centre International de Mathématiques Pures et Appliquées’ research in pairs fellowship and a partial grant from Ilam University.