Algèbres de dimension finie dont le carré du radical de la catégorie des modules est nul
Bibliographic record
Abstract
Dans ce mémoire, on entend par algèbre toute k-algèbre de dimension finie sur un corps commutatif algébriquement clos k. Si A est une k-algèbre, on entend par A-module tout A-module à gauche de type fini, sauf si spécifié autrement. Après avoir introduit les notions nécessaires de la théorie des catégories, nous présentons la définition du radical de la catégorie des modules. Par la suite, nous exposons certains concepts de la théorie des représentations des algèbres, notamment les morphismes presque scindés dans le but de démontrer le théorème suivant : Théorème : Soit A = kQ/I, où Q est un carquois connexe et I un idéal admissible denkQ. Alors rad^2(modA) = 0 si et seulement si Q se compose d’un point ou d’une flèche entre deux points distincts.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".