Bibliographic record
Abstract
Abstract Let ε be an injectively resolving subcategory of left R-modules. A left R-module M (resp. right R-module N) is called ε-injective (resp. ε-flat) if Ext1R (G,M) = 0 (resp. TorR1 (N, G) = 0) for any G ∊ ε. Let ε be a covering subcategory. We prove that a left R-module M is E-injective if and only if M is a direct sum of an injective left R-module and a reduced E-injective left R-module. Suppose ℱ is a preenveloping subcategory of right R-modules such that ε+ ⊆ ℱ and ℱ+ ⊆ ε. It is shown that a finitely presented right R-module M is ε-flat if and only if M is a cokernel of an ℱ-preenvelope of a right R-module. In addition, we introduce and investigate the ε-injective and ε-flat dimensions of modules and rings. We also introduce ε-(semi)hereditary rings and ε-von Neumann regular rings and characterize them in terms of ε-injective and ε-flat modules.
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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 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".