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Record W4256640869 · doi:10.1142/s0219498817501663

D4-Modules

2016· article· en· W4256640869 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueJournal of Algebra and Its Applications · 2016
Typearticle
Languageen
FieldMathematics
TopicRings, Modules, and Algebras
Canadian institutionsMemorial University of Newfoundland
FundersNanjing UniversityNatural Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of ChinaOhio State University
KeywordsMathematicsHomomorphismProperty (philosophy)Class (philosophy)Algebra over a fieldCombinatoricsDiscrete mathematicsPure mathematicsComputer science

Abstract

fetched live from OpenAlex

A module [Formula: see text] is called a [Formula: see text]-module if, whenever [Formula: see text] and [Formula: see text] are submodules of [Formula: see text] with [Formula: see text] and [Formula: see text] is a homomorphism with [Formula: see text], we have [Formula: see text]. The class of [Formula: see text]-modules contains the [Formula: see text]-modules as well as the dual-square-free (DSF) modules. Furthermore, a [Formula: see text]-module [Formula: see text] is called pseudo-discrete if [Formula: see text] is also a lifting module. In this paper, we study the [Formula: see text]-, the DSF, and the pseudo-discrete modules, and show that a pseudo-discrete module is clean iff it has the finite exchange property iff it has the full exchange property.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.073
Threshold uncertainty score0.238

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.029
GPT teacher head0.286
Teacher spread0.257 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it