{"paper":{"title":"Laurent cancellation for rings of transcendence degree one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Gene Freudenburg","submitted_at":"2013-09-18T18:31:12Z","abstract_excerpt":"If $R$ is an integral domain and $A$ is an $R$-algebra, then $A$ has the {\\it Laurent cancellation property over $R$} if $A^{[\\pm n]}\\cong_RB^{[\\pm n]}$ implies $A\\cong_RB$ ($n\\ge 0$ and $B$ an $R$-algebra). Here, $A^{[\\pm n]}$ denotes the ring of Laurent polynomials in $n$ variables over $A$. Our main result (Thm. 4.3) is that, if the transcendence degree of $A$ over $R$ is one, then $A$ has the Laurent cancellation property. The proof uses the characterization of Laurent polynomial rings given in Thm. 3.2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4737","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"}