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$k$-Gorenstein Modules

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Zhaoyong Huang

Rings and Algebras · Submitted 10 Sep 2004

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

The authors' main claim In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize it in terms of the $U$-resolution dimension of some special injective modules and the property of the functors ${\rm Ext}^{i}({\rm Ext}^{i}(-, U), U)$ preserving monomorphisms, which develops a classical result of Auslander.

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arXiv IDmath/0409177 (version 2)
Pith ID32N4DS43, Pith's permanent record of this paper and its review
CitationZhaoyong Huang. "$k$-Gorenstein Modules." arXiv:math/0409177 (2004). https://pith.science/paper/32N4DS43
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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, 3,729 input tokens.

What the abstract itself states, as probabilities: claims first 0.18 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.80 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize it in terms of the $U$-resolution dimension of some special injective modules and the property of the functors ${\rm Ext}^{i}({\rm Ext}^{i}(-, U), U)$ preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of $_{\Lambda}U_{\Gamma}$ with finite left or right injective dimension.

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 Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. background 1.00 0.07 0.02 asserted 0.82
s1 In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize it in terms of the $U$-resolution dimension of some special injective modules and the property of the functors ${\rm Ext}^{i}({\rm Ext}^{i}(-, U), U)$ preserving monomorphisms, which develops a classical result of Auslander. contribution 0.99 0.96 0.70 asserted 1.00
s2 As an application, we study the properties of dual modules relative to Gorenstein bimodules. contribution 1.00 0.92 0.08 asserted 0.92
s3 In addition, we give some properties of $_{\Lambda}U_{\Gamma}$ with finite left or right injective dimension. contribution 0.79 0.89 0.04 asserted 0.96

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

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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

Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize it in terms of the $U$-resolution dimension of some special injective modules and the property of the functors ${\rm Ext}^{i}({\rm Ext}^{i}(-, U), U)$ preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of $_{\Lambda}U_{\Gamma}$ with finite left or right injective dimension.

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