{"paper":{"title":"On Maximal Subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Immanuel Stampfli, Stefan Maubach","submitted_at":"2015-01-15T17:38:41Z","abstract_excerpt":"Let $\\textbf{k}$ be an algebraically closed field. We classify all maximal $\\textbf{k}$-subalgebras of any one-dimensional finitely generated $\\textbf{k}$-domain. In dimension two, we classify all maximal $\\textbf{k}$-subalgebras of $\\textbf{k}[t, t^{-1}, y]$. To the authors' knowledge, this is the first such classification result for an algebra of dimension $> 1$. In the course of this study, we classify also all maximal $\\textbf{k}$-subalgebras of $\\textbf{k}[t, y]$ that contain a coordinate. Furthermore, we give examples of maximal $\\textbf{k}$-subalgebras of $\\textbf{k}[t, y]$ that do not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03753","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":""},"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"}