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Record W2010252940 · doi:10.1080/00927870902747241

Strictly Stratified Algebras Revisited

2009· article· en· W2010252940 on OpenAlexafffund
Charles Paquette

Bibliographic record

VenueCommunications in Algebra · 2009
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversité de Sherbrooke
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsEndomorphismConjectureAlgebra over a fieldPure mathematics

Abstract

fetched live from OpenAlex

In [1 Ágoston , I. , Dlab , V. , Lukács , E. ( 2000 ). Strictly Stratified Algebras. Algebra Proc. Intern. Alg. Conf. on the Occassion of the 90th Birthday of A. G. Kurosh , Moscow , 1998 , pp. 17 – 26 . [Google Scholar]], Ágoston, Dlab, and Lukács introduced the notion of strictly stratified algebras. These algebras are stratified in the sense of Cline, Parshall, and Scott (see [5 Cline , E. , Parshall , B. J. , Scott , L. L. ( 1996 ). Stratifying endomorphism algebras . Memoirs of the AMS 124 . no. 591 . viii+119 pp .[Crossref], [Web of Science ®] , [Google Scholar]]) and contain the well-known class of standardly stratified algebras. The latter is well described from a homological point of view. Indeed, many homological conjectures such as the finitistic dimension conjectures (see [2 Ágoston , I. , Happel , D. , Lukács , E. , Unger , L. ( 2000 ). Finitistic dimension of standardly stratified algebras . Comm. Algebra 28 : 2745 – 2752 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]), the Cartan determinant conjecture (see [10 Wick , D. D. ( 1996 ). A generalization of quasi-hereditary rings . Comm. Algebra 24 ( 4 ): 1217 – 1227 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]) and the strong no loop conjecture (see [9 Liu , S. , Paquette , C. ( 2006 ). Some homological conjectures for quasi-stratified algebras . J. Algebra 301 : 240 – 255 .[Crossref], [Web of Science ®] , [Google Scholar]]) hold true for standardly stratified algebras. In this article, we shall try to extend these results to strictly stratified algebras. The key idea is to show that the filtration condition of a strictly stratified algebra behaves well with respect to the extension groups. As main results, we establish the finitistic injective dimension conjecture, verify the Cartan determinant conjecture and its converse, and prove a weaker version of the strong no loop conjecture for strictly stratified algebras.

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation 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: none
Teacher disagreement score0.010
Threshold uncertainty score0.034

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.002
Science and technology studies0.0020.003
Scholarly communication0.0030.005
Open science0.0010.002
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0100.001

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 head0.070
GPT teacher head0.353
Teacher spread0.283 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations2
Published2009
Admission routes2
Has abstractyes

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