{"id":"W2154157897","doi":"10.1142/s0219498812501599","title":"MODULES WHICH ARE INVARIANT UNDER AUTOMORPHISMS OF THEIR INJECTIVE HULLS","year":2012,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":95,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"National Taiwan University; National Science Council; Natural Sciences and Engineering Research Council of Canada; National Center for Theoretical Sciences","keywords":"Automorphism; Injective function; Mathematics; Invariant (physics); Horizontal line test; Injective module; Divisible group; Pure mathematics; Discrete mathematics; Geometry; Cyclic group","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004811643,0.0001508855,0.0003713984,0.0001461355,0.0001203802,0.00002654481,0.0002007371,0.00009346045,0.00005063458],"category_scores_gemma":[0.0001296662,0.0001115759,0.00009397675,0.0002471404,0.00006014464,0.0003456479,0.00005651018,0.0002212048,0.000008646713],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003227608,"about_ca_system_score_gemma":0.00005823081,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003040821,"about_ca_topic_score_gemma":0.000006968558,"domain_scores_codex":[0.9988646,0.00005060049,0.0005443959,0.00011633,0.000216943,0.0002071249],"domain_scores_gemma":[0.9980472,0.0003225149,0.0007936748,0.000219049,0.0004553083,0.0001622267],"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":[0.0000196081,0.000677546,0.001474625,0.0001262611,0.0002584431,6.588726e-7,0.002303883,0.00001439863,0.0110242,0.9798221,0.002081454,0.002196812],"study_design_scores_gemma":[0.0008378059,0.0001625015,0.06528487,0.0002168441,0.0002501193,0.0002513967,0.002581738,0.0001859683,0.03294579,0.8944971,0.002474344,0.000311534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.97488,0.001972593,0.02072101,0.001061125,0.00009083006,0.0003120205,0.0000282423,0.0000210144,0.0009131008],"genre_scores_gemma":[0.9946334,0.0003193858,0.004481853,0.0000945951,0.0003414335,0.00001931789,0.000001673472,0.00002304468,0.00008523827],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08532503,"threshold_uncertainty_score":0.4549933,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03945046491031283,"score_gpt":0.2802798820632766,"score_spread":0.2408294171529637,"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."}}