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Record W2022096905 · doi:10.1142/s0219498808003089

LEFT QUASI-MORPHIC RINGS

2008· article· en· W2022096905 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

VenueJournal of Algebra and Its Applications · 2008
Typearticle
Languageen
FieldMathematics
TopicRings, Modules, and Algebras
Canadian institutionsUniversity of Calgary
Fundersnot available
KeywordsAnnihilatorMathematicsPrincipal ideal ringRing (chemistry)Von Neumann regular ringPrimitive ringIdeal (ethics)Characterization (materials science)Principal idealPure mathematicsCombinatoricsReduced ringDiscrete mathematicsCommutative ringAlgebra over a fieldCommutative propertyPhysics

Abstract

fetched live from OpenAlex

A ring R is called left quasi-morphic if, for each a ∈ R, there exist b and c in R such that Ra = l (b) and l (a) = Rc (where l (x) is the left annihilator). Every (von Neumann) regular ring is left quasi-morphic, as is every left morphic ring (b = c above). The main theorem of this paper is that, in a left quasi-morphic ring, finite intersections and finite sums of principal left ideals are again principal. This leads to structure theorems when mild finiteness conditions are imposed. In an earlier paper, the first two authors showed that left and right quasi-morphic rings have both these properties (on both sides), and used this to give a new characterization of the artinian principal ideal rings: They are just the left and right quasi-morphic rings with ACC on principal annihilators r (a), a ∈ R. Some extensions of this result are presented here.

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 score0.139
Threshold uncertainty score0.416

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 head0.038
GPT teacher head0.280
Teacher spread0.242 · 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