Why this work is in the frame
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Bibliographic record
Abstract
A ring [Formula: see text] is called left comorphic if, for each [Formula: see text] there exists [Formula: see text] such that [Formula: see text] and [Formula: see text] Examples include (von Neumann) regular rings, and [Formula: see text] for a prime [Formula: see text] and [Formula: see text] One motivation for studying these rings is that the comorphic rings (left and right) are just the quasi-morphic rings, where [Formula: see text] is left quasi-morphic if, for each [Formula: see text] there exist [Formula: see text] and [Formula: see text] in [Formula: see text] such that [Formula: see text] and [Formula: see text] If [Formula: see text] here the ring is called left morphic. It is shown that [Formula: see text] is left comorphic if and only if, for any finitely generated left ideal [Formula: see text] there exists [Formula: see text] such that [Formula: see text] and [Formula: see text] Using this, we characterize when a left comorphic ring has various properties, and show that if [Formula: see text] is local with nilpotent radical, then [Formula: see text] is left comorphic if and only if it is right comorphic. We also show that a semiprime left comorphic ring [Formula: see text] is semisimple if either [Formula: see text] is left perfect or [Formula: see text] has the ACC on [Formula: see text] After a preliminary study of left comorphic rings with the ACC on [Formula: see text] we show that a quasi-Frobenius ring is left comorphic if and only if every right ideal is principal; if and only if every left ideal is a left principal annihilator. We characterize these rings as follows: The following are equivalent for a ring [Formula: see text] [Formula: see text] is quasi-Frobenius and left comorphic. [Formula: see text] is left comorphic, left perfect and right Kasch. [Formula: see text] is left comorphic, right Kasch, with the ACC on [Formula: see text] [Formula: see text] is left comorphic, left mininjective, with the ACC on [Formula: see text] Some examples of these rings are given.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it