{"id":"W4288112285","doi":"10.48550/arxiv.1909.04023","title":"Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin,\\n and Heinzer","year":2019,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Noncommutative geometry; Commutative property; Polynomial ring; Counterexample; Discrete mathematics; Pure mathematics; Algebra over a field; Polynomial; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0022167,0.0003130563,0.0005171219,0.000993938,0.001997831,0.001569863,0.001054375,0.0006264622,0.007248393],"category_scores_gemma":[0.004375684,0.0003080137,0.0008774236,0.0006655628,0.002685763,0.004224416,0.003132767,0.001843132,0.0008039744],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00083693,"about_ca_system_score_gemma":0.0009371673,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001091645,"about_ca_topic_score_gemma":0.0009917071,"domain_scores_codex":[0.998951,0.0001882371,0.00008082739,0.0002233656,0.0004135678,0.0001429777],"domain_scores_gemma":[0.9975533,0.0009643831,0.0002767899,0.0003517403,0.0006355712,0.0002181349],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003441829,0.00002488479,0.0003573148,0.00004143588,0.00001004616,0.0001089051,0.0003432957,0.0003827764,0.001158917,0.9929031,0.0013547,0.003280286],"study_design_scores_gemma":[0.00005605073,0.00003959429,0.0006708385,0.00001812061,0.00001790758,0.0002886096,0.0001543554,0.003916151,0.00308933,0.970456,0.02127024,0.00002282987],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2913852,0.004268756,0.35617,0.007415766,0.001681658,0.0001847102,0.0005663778,0.0004457964,0.3378817],"genre_scores_gemma":[0.9088902,0.0008777804,0.03974481,0.001786715,0.0005750972,0.0001176624,0.0003391599,0.0001013439,0.04756724],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007248393,"threshold_uncertainty_score":0.0242483,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08530868551890251,"score_gpt":0.2252217265648694,"score_spread":0.1399130410459669,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}