Representation Extension and Amalgamation in Pomonoids
Bibliographic record
Abstract
Flatness properties of acts over monoids and their connection with monoid amalgamation have been investigated for almost four decades and a substantial literature on the subject has now appeared. Analogous research, concerning the action of partially ordered monoids on partially ordered sets and its relation to pomonoid amalgamation, was begun in 1980s in two articles by S. M. Fakhruddin. The subject then remained dormant until the recent past when several articles on flatness in the setting of ordered monoids acting on posets (briefly, S-posets) appeared. It has now been established that the introduction of order results in severe restrictions as far as absolute flatness is concerned. Also, after formulating in the ordered context the Representation Extension and Right Congruence Extension Properties, first used by T. E. Hall to study semigroup amalgams, the authors recently observed in their article [4 Bulman-Fleming , S. , Nasir , S. ( 2010 ). Examples concerning absolute flatness and amalgamation in pomonoids . Semigroup Forum 80 : 272 – 292 .[Crossref], [Web of Science ®] , [Google Scholar]] that inverse monoids, though being amalgamation bases in the class of all monoids, may fail to possess this property when put in the ordered scenario. The purpose of the present article is to formulate an ordered version of the Strong Representation Extension Property of Hall and to explore its connections with absolute flatness and amalgamation of pomonoids. This enables us to prove that pogroups are (strong) amalgamation bases in the class of all pomonoids.
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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 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".