{"id":"W2092354042","doi":"10.1142/s0219498815500024","title":"Finite commutative rings with higher genus unit graphs","year":2014,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"Natural Sciences and Engineering Research Council of Canada; Natural Science Foundation of Guangxi Province; National Natural Science Foundation of China","keywords":"Mathematics; Combinatorics; Commutative ring; Vertex (graph theory); Isomorphism (crystallography); Unit (ring theory); Graph; Discrete mathematics; Genus; Commutative property; Chemistry; Crystallography","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004064646,0.0003257608,0.0003673741,0.001436595,0.0005969873,0.001471362,0.0005908247,0.0003806696,0.002504448],"category_scores_gemma":[0.001561267,0.0002305999,0.0004420364,0.0006397521,0.001542231,0.0019644,0.001248324,0.0005518069,0.000231037],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005203692,"about_ca_system_score_gemma":0.0002018157,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005513936,"about_ca_topic_score_gemma":0.0004458004,"domain_scores_codex":[0.9995858,0.00007470104,0.00002594653,0.00008126845,0.00007700735,0.0001552547],"domain_scores_gemma":[0.9986492,0.000514071,0.0003569726,0.0001562224,0.00007065238,0.0002529773],"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":[0.0002837899,0.0001054068,0.01188487,0.0001531647,0.00004198335,0.001260329,0.001901916,0.008183692,0.01768315,0.9315233,0.0008875623,0.02609091],"study_design_scores_gemma":[0.00009579326,0.0002134173,0.03446013,0.0001137518,0.0001679801,0.003500263,0.002580765,0.03044445,0.03175984,0.8803792,0.01618451,0.00009987901],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9830813,0.0002464689,0.008256166,0.00004663816,0.000009709289,0.000009200323,0.00005952438,0.00009401295,0.008196962],"genre_scores_gemma":[0.9967944,0.0001221828,0.002299751,0.00001547476,0.00001224764,0.000007708077,0.00006137558,0.0000121327,0.0006748543],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002504448,"threshold_uncertainty_score":0.008378208,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03028950731652571,"score_gpt":0.2781866535436117,"score_spread":0.2478971462270859,"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."}}