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Record W1966760252 · doi:10.1142/s1005386711000101

On Duo Group Rings

2011· article· en· W1966760252 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.

Bibliographic record

VenueAlgebra Colloquium · 2011
Typearticle
Languageen
FieldMathematics
TopicRings, Modules, and Algebras
Canadian institutionsBrock University
Fundersnot available
KeywordsMathematicsIntegral domainGroup ringRing (chemistry)QuotientGroup (periodic table)Ring of integersOrder (exchange)Torsion (gastropod)Quotient ringField (mathematics)Pure mathematicsAlgebraic numberBrauer groupZero (linguistics)Global fieldAlgebraic number fieldCombinatoricsMathematical analysisCommutative ring

Abstract

fetched live from OpenAlex

It is shown that if the group ring RQ 8 of the quaternion group Q 8 of order 8 over an integral domain R is duo, then R is a field for the following cases: (1) char R ≠ 0, and (2) char R = 0 and S ⊆ R ⊆ K S , where S is a ring of algebraic integers and K S is its quotient field. Hence, we confirm that the field ℚ of rational numbers is the smallest integral domain R of characteristic zero such that RQ 8 is duo. A non-field integral domain R of characteristic zero for which RQ 8 is duo is also identified. Moreover, we give a description of when the group ring RG of a torsion group G is duo.

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 categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
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 score0.105
Threshold uncertainty score1.000

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)0.0010.001

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 head0.040
GPT teacher head0.256
Teacher spread0.215 · 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