{"id":"W2059205268","doi":"10.1016/j.jpaa.2010.02.019","title":"Ring ideals and the Stone-Čech compactification in pointfree topology","year":2010,"lang":"en","type":"article","venue":"Journal of Pure and Applied Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Compactification (mathematics); Pure mathematics; Ring (chemistry); Bounded function; Lattice (music); Topology (electrical circuits); Frame (networking); Discrete mathematics; Algebra over a field; Combinatorics; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.001159188,0.0001161354,0.0003450241,0.000108545,0.00009339485,0.00006503965,0.0001543919,0.00009450028,0.00003241045],"category_scores_gemma":[0.0001445661,0.00007296685,0.00004503963,0.00007936802,0.000196924,0.0001030798,0.0000442352,0.0005671944,0.000002179611],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009852971,"about_ca_system_score_gemma":0.00002377696,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008617265,"about_ca_topic_score_gemma":0.0001114914,"domain_scores_codex":[0.9990848,0.00004196512,0.0004404768,0.000117287,0.0001551382,0.0001603365],"domain_scores_gemma":[0.9989416,0.0004151609,0.0003617949,0.0001669716,0.0000435223,0.00007093509],"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":[0.0001261768,0.00006214001,0.0009246957,0.00003509707,0.00003786396,0.000006227538,0.001698995,0.000001521447,0.01759466,0.9690989,0.0005541513,0.009859552],"study_design_scores_gemma":[0.00261932,0.0000423069,0.01868993,0.00003620184,0.00005539735,0.0002766991,0.001449219,0.00005049533,0.005508063,0.9704517,0.0006818249,0.0001389103],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.995074,0.0002333981,0.0004224585,0.002090359,0.0001492665,0.0001532254,8.507845e-7,0.000008550863,0.001867924],"genre_scores_gemma":[0.9971986,0.00009848677,0.002166731,0.0001849097,0.0002893016,0.000003956825,3.735818e-7,0.00001253503,0.00004507895],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01776523,"threshold_uncertainty_score":0.2975502,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02225247523826116,"score_gpt":0.2813053636334734,"score_spread":0.2590528883952122,"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."}}