{"id":"W7117428386","doi":"10.61091/um125-06","title":"Zero divisor graph of endomorphism ring of direct product of groups","year":2025,"lang":"","type":"article","venue":"Utilitas Mathematica","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Zero divisor; Endomorphism; Direct product; Divisor (algebraic geometry); Graph; Endomorphism ring; Prime (order theory)","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002402448,0.0007966198,0.003100642,0.0008544347,0.0001478091,0.0000306441,0.001140728,0.0002661817,0.0005808077],"category_scores_gemma":[0.004918428,0.0007398357,0.00103693,0.001286215,0.001321306,0.0002469459,0.0006202334,0.0004159493,0.00002646765],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006798696,"about_ca_system_score_gemma":0.0002512374,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005121015,"about_ca_topic_score_gemma":0.000009592385,"domain_scores_codex":[0.9930956,0.0003291623,0.003804346,0.0009143053,0.001043121,0.0008134624],"domain_scores_gemma":[0.9915082,0.003039389,0.002046938,0.002628978,0.0006163287,0.0001601218],"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":[0.0002488152,0.00595992,0.000910646,0.0648632,0.002197314,0.000009550163,0.01287577,0.00001259393,0.02971881,0.8750966,0.002902389,0.005204347],"study_design_scores_gemma":[0.001503048,0.000300743,0.0008684265,0.007751317,0.001331637,0.000009833353,0.001190092,0.0006076257,0.2794178,0.7063149,0.0002086093,0.0004960746],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8984948,0.008941986,0.01199573,0.0002575971,0.0008103913,0.002847732,0.0002990759,0.0001314148,0.07622122],"genre_scores_gemma":[0.9794229,0.0004132637,0.0181446,0.00001566728,0.00005698612,0.00007208272,0.000007284639,0.00009559798,0.001771565],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.249699,"threshold_uncertainty_score":0.9995053,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02713196743380609,"score_gpt":0.2709110189277085,"score_spread":0.2437790514939024,"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."}}