{"id":"W2047974109","doi":"10.1142/s0219498812501277","title":"ON RINGS OVER WHICH THE INJECTIVE HULL OF EACH CYCLIC MODULE IS Σ-EXTENDING","year":2012,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"McMaster University","keywords":"Mathematics; Injective function; Hull; Ring (chemistry); Class (philosophy); Injective module; Von Neumann regular ring; Combinatorics; Pure mathematics; Computer science; Artificial intelligence; Composite material","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005229101,0.0001341938,0.0002577994,0.0001246062,0.000187384,0.00003073283,0.0002241604,0.00006775314,0.00006963188],"category_scores_gemma":[0.0001830633,0.00008873844,0.0001012334,0.0002507904,0.00004868178,0.0002840658,0.00005205135,0.0002915834,0.00001297926],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003393715,"about_ca_system_score_gemma":0.00002833585,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004460681,"about_ca_topic_score_gemma":0.000001964045,"domain_scores_codex":[0.9989058,0.00003775686,0.0004484509,0.0001159993,0.0002834482,0.0002085153],"domain_scores_gemma":[0.9984447,0.0004367428,0.0005541823,0.0002421664,0.0002105846,0.0001116128],"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":[0.00002989968,0.0005345975,0.002591819,0.00008764263,0.0001881763,3.203838e-7,0.004271863,0.000005835508,0.006335576,0.9770595,0.005186982,0.00370776],"study_design_scores_gemma":[0.001349083,0.0003915583,0.1155034,0.0003070862,0.000450691,0.0001980018,0.001541295,0.000326941,0.04716694,0.8170227,0.01524501,0.0004973544],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9933178,0.000903718,0.0025035,0.0006907069,0.00007248695,0.0002489737,0.000008680371,0.00001081822,0.002243275],"genre_scores_gemma":[0.9981444,0.0002541551,0.0008075578,0.0001974737,0.0003568478,0.00001972572,6.275145e-7,0.00002142463,0.0001977934],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1600368,"threshold_uncertainty_score":0.3618649,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02775361495949954,"score_gpt":0.3025897242793623,"score_spread":0.2748361093198628,"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."}}