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Record W4244816701 · doi:10.4153/cmb-2010-065-9

Hulls of Ring Extensions

2010· article· en· W4244816701 on OpenAlex
Gary F. Birkenmeier, Jae Keol Park, S. Tariq Rizvi

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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCanadian Mathematical Bulletin · 2010
Typearticle
Languageen
FieldMathematics
TopicRings, Modules, and Algebras
Canadian institutionsnot available
FundersUniversity of Louisiana at LafayetteTulane UniversityOhio State University
KeywordsMathematicsMorita equivalenceAbelian groupPure mathematicsNoncommutative ringRing (chemistry)Primitive ringPrincipal ideal ringCommutative ringGroup ringSemiprime ringSemiprimeReduced ringCommutative propertyRadical of a ringGroup (periodic table)Combinatorics

Abstract

fetched live from OpenAlex

Abstract We investigate the behavior of the quasi-Baer and the right FI-extending right ring hulls under various ring extensions including group ring extensions, full and triangular matrix ring extensions, and infinite matrix ring extensions. As a consequence, we show that for semiprime rings R and S , if R and S are Morita equivalent, then so are the quasi-Baer right ring hulls of R and S , respectively. As an application, we prove that if unital C *-algebras A and B are Morita equivalent as rings, then the bounded central closure of A and that of B are strongly Morita equivalent as C *-algebras. Our results show that the quasi-Baer property is always preserved by infinite matrix rings, unlike the Baer property. Moreover, we give an affirmative answer to an open question of Goel and Jain for the commutative group ring A [ G ] of a torsion-free Abelian group G over a commutative semiprime quasi-continuous ring A . Examples that illustrate and delimit the results of this paper are provided.

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)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient 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 score0.082
Threshold uncertainty score0.997

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.002
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)0.0190.004

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 head0.026
GPT teacher head0.257
Teacher spread0.231 · 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