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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.4737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-18T18:31:12Z","cross_cats_sorted":[],"title_canon_sha256":"2cc0d92720651b70673eb24f4026a598e508131304e7daba37d605120478c273","abstract_canon_sha256":"8c8da31650315c0dcfc06bd531fc8cd4d62b9daf081d420f43102e5e22035ff9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:57.010567Z","signature_b64":"U5N2K1FEqQa8o/jZy4xtISgkclxaRxdh/z/MoHDBLg0ZJQVShlKrI6ivdLL+UWiyuNRPn6u7pRihTcqTANsvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28a807668c151d2caf36fa22f663c2ec13d3105ce310f094921370fb9987efef","last_reissued_at":"2026-05-18T03:11:57.009829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:57.009829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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