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The Schr\"{o}der-Bernstein problem for Modules

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Pedro A. Guil Asensio, Berke Kalebog̃az, Ashish K. Srivastava

Rings and Algebras · Submitted 14 Mar 2017

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

The authors' main claim We obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes.

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arXiv ID1703.04787 (version 1)
Pith IDHMTH2CDI, Pith's permanent record of this paper and its review
CitationAshish K. Srivastava, Berke Kalebo\~gaz, Pedro A. Guil Asensio. "The Schr\"{o}der-Bernstein problem for Modules." arXiv:1703.04787 (2017). https://pith.science/paper/HMTH2CDI
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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, 3,098 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.14 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we study the Schr\"{o}der-Bernstein problem for modules. We obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schr\"{o}der-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes.

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 In this paper we study the Schr\"{o}der-Bernstein problem for modules. contribution 0.73 0.80 0.04 asserted 0.58
s1 We obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. result 0.98 0.95 0.77 asserted 1.00
s2 In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schr\"{o}der-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes. result 0.98 0.94 0.24 asserted 1.00

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

What was examined, and what was not

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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

In this paper we study the Schr\"{o}der-Bernstein problem for modules. We obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schr\"{o}der-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes.

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