{"paper":{"title":"Rings of Teter type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J\\\"urgen Herzog, Oleksandra Gasanova, Somayeh Moradi, Takayuki Hibi","submitted_at":"2021-12-08T11:32:05Z","abstract_excerpt":"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 $\\varphi(\\omega_R)$ with $\\varphi\\in Hom_R(\\omega_R,R)$. The smallest number $s$ for which there exist $\\varphi_1, \\ldots, \\varphi_s \\in Hom_R(\\omega_R,R)$ with $tr(\\omega_R)=\\varphi_1(\\omega_R) + \\cdots + \\varphi_s(\\omega_R)$ 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 Gore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04237","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.04237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}