Green's Relations on the Monoid of Regular Hypersubstitutions
Bibliographic record
Abstract
The theory of hyperidentities and hypervarieties is based on the fact that the set Hyp (τ) of all hypersubstitutions of a fixed type τ forms a monoid, with a Galois connection between submonoids of this monoid and complete sublattices of the lattice of all varieties of type τ. For this reason, there is interest in studying the semigroup or monoid properties of Hyp (τ) and its submonoids. One approach is to study the five relations known as Green's relations definable on any semigroup. In this paper, we consider the type τ = (n) with one n-ary operation symbol for n≥ 1, and the submonoid Reg (n) of regular hypersubstitutions. We characterize Green's relations on every subsemigroup of Reg (n); then using this characterization we describe which subsemigroups of Reg (n) are 𝒢-subsemigroups of Reg (n) defined by Levi.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".