{"id":"W2267849513","doi":"10.1007/978-0-387-21690-4_1","title":"Unique Factorization Domains, Ideals, and Principal Ideal Domains","year":2001,"lang":"en","type":"book-chapter","venue":"Universitext","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Unique factorization domain; Principal ideal; Commutative ring; Mathematics; Unit (ring theory); Ideal (ethics); Pure mathematics; Quotient; Factorization; Integral domain; Field (mathematics); Ring (chemistry); Principal ideal ring; Maximal ideal; Principal (computer security); Zero (linguistics); Algebra over a field; Domain (mathematical analysis); Commutative property; Combinatorics; Computer science; Mathematical analysis; Algorithm; Philosophy","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001429637,0.0004404195,0.000483878,0.0003247534,0.0002282856,0.00005958326,0.0002559066,0.0005122542,0.0008486216],"category_scores_gemma":[0.00003575436,0.0004697013,0.0001440772,0.00005190856,0.0001549459,0.0001984128,0.0001995369,0.0003941968,0.00008623363],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002746299,"about_ca_system_score_gemma":0.00009073858,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004463457,"about_ca_topic_score_gemma":0.0001472016,"domain_scores_codex":[0.9985048,0.00002936076,0.0003078023,0.0004984335,0.0003423093,0.0003173021],"domain_scores_gemma":[0.9987569,0.0001733873,0.0003223495,0.0004442212,0.0001078298,0.0001953127],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00002427136,0.00001909593,0.0001044785,0.000109888,0.0001120678,0.0001735469,0.0005952333,0.000001491157,0.0000306513,0.992839,0.004311572,0.001678688],"study_design_scores_gemma":[0.000550601,0.00005673629,0.00008910479,0.0002002334,0.0001429843,0.00003253763,0.0001127492,0.00001082026,0.00002114798,0.3705758,0.6277427,0.0004645924],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01191654,0.0002811444,0.00885357,0.0001141005,0.0002417004,0.0004965605,0.00009258296,0.0002346683,0.9777691],"genre_scores_gemma":[0.03998845,0.002504501,0.003620103,0.0001656452,0.000580229,0.000001651893,0.0002116874,0.0001812835,0.9527465],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.6234311,"threshold_uncertainty_score":0.9997755,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02474793681246978,"score_gpt":0.2381770370907119,"score_spread":0.2134291002782422,"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."}}