Bibliographic record
Abstract
Auslander and Smalø (Auslander, M., Smalø, S. O. (1980). Preprojective modules over artin algebras. J. Algebra 66:61–122) introduced and studied extensively preprojective modules and preinjective modules over an artin algebra. We now call a module hereditarily preprojective or hereditarily preinjective if its submodules are all preprojective or its quotient modules are all preinjective, respectively. Coelho (Coelho, F. U. (1993). Components of Auslander-Reiten quivers with only preprojective modules. J. Algebra 157: 472–488) studied Auslander-Reiten components containing only hereditarily preprojective modules and gave a number of characterizations of such components. We shall study further these modules by using the description of shapes of semi-stable Auslander-Reitan components; see Liu (Liu, S. (1992). Degrees of irreducible maps and the shapes of Auslander-Reiten quivers. J. London Math. Soc. 45(2):32–54; Liu, S. (1993). Semi-stable components of an Auslander-Reiten quiver. J. London Math. Soc. 47(2):405–416). Our results will imply the result of Coelho (Coelho, F. U. (1993). Components of Auslander-Reiten quivers with only preprojective modules. J. Algebra 157: 472–488, (1.2)) and that of Auslander-Smalø (Auslander, M. and Smalø, S. O. (1980). Preprojective modules over artin algebras, J. Algebra 66:61–122, (9.16)). As an application, moreover, we shall show that a stable Auslander-Reiten component with “few” stable maps in TrD-direction is of shape ℤA ∞.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".