Bibliographic record
Abstract
In [1 Ágoston , I. , Dlab , V. , Lukács , E. ( 2000 ). Strictly Stratified Algebras. Algebra Proc. Intern. Alg. Conf. on the Occassion of the 90th Birthday of A. G. Kurosh , Moscow , 1998 , pp. 17 – 26 . [Google Scholar]], Ágoston, Dlab, and Lukács introduced the notion of strictly stratified algebras. These algebras are stratified in the sense of Cline, Parshall, and Scott (see [5 Cline , E. , Parshall , B. J. , Scott , L. L. ( 1996 ). Stratifying endomorphism algebras . Memoirs of the AMS 124 . no. 591 . viii+119 pp .[Crossref], [Web of Science ®] , [Google Scholar]]) and contain the well-known class of standardly stratified algebras. The latter is well described from a homological point of view. Indeed, many homological conjectures such as the finitistic dimension conjectures (see [2 Ágoston , I. , Happel , D. , Lukács , E. , Unger , L. ( 2000 ). Finitistic dimension of standardly stratified algebras . Comm. Algebra 28 : 2745 – 2752 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]), the Cartan determinant conjecture (see [10 Wick , D. D. ( 1996 ). A generalization of quasi-hereditary rings . Comm. Algebra 24 ( 4 ): 1217 – 1227 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]) and the strong no loop conjecture (see [9 Liu , S. , Paquette , C. ( 2006 ). Some homological conjectures for quasi-stratified algebras . J. Algebra 301 : 240 – 255 .[Crossref], [Web of Science ®] , [Google Scholar]]) hold true for standardly stratified algebras. In this article, we shall try to extend these results to strictly stratified algebras. The key idea is to show that the filtration condition of a strictly stratified algebra behaves well with respect to the extension groups. As main results, we establish the finitistic injective dimension conjecture, verify the Cartan determinant conjecture and its converse, and prove a weaker version of the strong no loop conjecture for strictly stratified algebras.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".