{"id":"W2607539787","doi":"10.1090/crmp/035/08","title":"The module structure of a group action on a polynomial ring: examples, generalizations, and applications","year":2004,"lang":"en","type":"book-chapter","venue":"CRM proceedings & lecture notes","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"Royal Military College of Canada; Queen's University","funders":"","keywords":"Group (periodic table); Mathematics; Pure mathematics; Polynomial ring; Algebra over a field; Action (physics); Ring (chemistry); Group action; Group ring; Polynomial; Computer science; Physics; Mathematical analysis; Chemistry","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":[0.00007678435,0.0004118491,0.0003790358,0.0001389871,0.0003999407,0.00008975047,0.0002687921,0.0004914952,0.0000302091],"category_scores_gemma":[0.000300026,0.0003162691,0.00009514568,0.00007647936,0.0001965464,0.00008164145,0.00008927561,0.0006152202,0.000001773396],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000171008,"about_ca_system_score_gemma":0.00005957785,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006285877,"about_ca_topic_score_gemma":0.00003671193,"domain_scores_codex":[0.9985682,0.000003990959,0.0004064663,0.0004749266,0.0003177107,0.0002286797],"domain_scores_gemma":[0.9985914,0.0002982316,0.0005782568,0.0002905286,0.0001742107,0.000067423],"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":[0.00002342785,0.00001428322,0.00001002903,0.0002277773,0.00006855702,2.227894e-7,0.0001984547,0.00002062634,0.0031023,0.9862978,0.00004096306,0.009995506],"study_design_scores_gemma":[0.0002365717,0.00007091915,0.00001710013,0.0001779502,0.0001234304,0.00001623759,0.00001219179,0.00002060196,0.006183522,0.9662729,0.026591,0.0002775797],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03697614,0.01207079,0.5094041,0.004060583,0.001816964,0.01386683,0.0008216692,0.001829186,0.4191537],"genre_scores_gemma":[0.9875388,0.0006101292,0.008557784,0.0001717625,0.001758866,0.0001085204,0.00007482426,0.0002239774,0.0009553826],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9505626,"threshold_uncertainty_score":0.999929,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03927566647674263,"score_gpt":0.2883312736550249,"score_spread":0.2490556071782823,"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."}}