{"paper":{"title":"Zariski Cancellation Problem for Noncommutative Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James J. Zhang, Jason Bell","submitted_at":"2016-01-18T17:57:16Z","abstract_excerpt":"A noncommutative analogue of the Zariski cancellation problem asks whether $A[x]\\cong B[x]$ implies $A\\cong B$ when $A$ and $B$ are noncommutative algebras. We resolve this affirmatively in the case when $A$ is a noncommutative finitely generated domain over the complex field of Gelfand-Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin-Schelter regular algebras of higher Gelfand-Kirillov dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04625","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"}