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Backstr\"om algebras

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Yuriy A. Drozd

Representation Theory · Submitted 26 Jun 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For the latter we define the global dimension, construct a sort of semi-orthogonal decomposition of the derived category and deduce that the derived dimension of a Backstr\"om ring is at most $2$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2206.12875 (version 2)
Pith IDJMRII75Y, Pith's permanent record of this paper and its review
CitationYuriy A. Drozd. "Backstr\"om algebras." arXiv:2206.12875 (2022). https://pith.science/paper/JMRII75Y
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,623 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We introduce Backstr\"om pairs and Backstr\"om rings, study their derived categories and construct for them a sort of categorical resolutions. For the latter we define the global dimension, construct a sort of semi-orthogonal decomposition of the derived category and deduce that the derived dimension of a Backstr\"om ring is at most $2$. Using this semi-orthogonal decomposition, we define a description of the module category as the category of elements of a special bimodule. We also construct a partial tilting for a Backstr\"om pair to a ring of triangular matrices and define the global dimension of the latter.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce Backstr\"om pairs and Backstr\"om rings, study their derived categories and construct for them a sort of categorical resolutions. contribution 1.00 0.97 0.18 asserted 0.99
s1 For the latter we define the global dimension, construct a sort of semi-orthogonal decomposition of the derived category and deduce that the derived dimension of a Backstr\"om ring is at most $2$. result 0.83 0.96 0.44 asserted 1.00
s2 Using this semi-orthogonal decomposition, we define a description of the module category as the category of elements of a special bimodule. contribution 0.83 0.95 0.11 asserted 1.00
s3 We also construct a partial tilting for a Backstr\"om pair to a ring of triangular matrices and define the global dimension of the latter. contribution 0.99 0.96 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce Backstr\"om pairs and Backstr\"om rings, study their derived categories and construct for them a sort of categorical resolutions. For the latter we define the global dimension, construct a sort of semi-orthogonal decomposition of the derived category and deduce that the derived dimension of a Backstr\"om ring is at most $2$. Using this semi-orthogonal decomposition, we define a description of the module category as the category of elements of a special bimodule. We also construct a partial tilting for a Backstr\"om pair to a ring of triangular matrices and define the global dimension of the latter.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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