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On the Lowey length of modules of finite projective dimension-II

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Tony J. Puthenpurakal

Commutative Algebra · Submitted 17 May 2023

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

The authors' main claim Then we show that necessarily $A$ is at worst a hypersurface singularity.

how it is stated · asserted 1.00 read the record →

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arXiv ID2305.10220 (version 1)
Pith IDTHMK3IQE, Pith's permanent record of this paper and its review
CitationTony J. Puthenpurakal. "On the Lowey length of modules of finite projective dimension-II." arXiv:2305.10220 (2023). https://pith.science/paper/THMK3IQE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,662 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.57 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let $(A,\mathfrak{m})$ be a Gorenstein local ring of dimension $d \geq 1$. Suppose there exists be a non-zero $A$ module $M$ of finite length and finite projective dimension such that $\ell\ell(M)$, the Lowey length of $M$, is equal to $\lambda(M)$, the length of $M$. Then we show that necessarily $A$ is at worst a hypersurface singularity. We also characterize Gorenstein local rings having a non-zero module $M$ of finite length and finite projective dimension with $\ell\ell(M) = \lambda(M)-1$.

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 $(A,\mathfrak{m})$ be a Gorenstein local ring of dimension $d \geq 1$. background 1.00 0.06 0.02 asserted 0.84
s1 Suppose there exists be a non-zero $A$ module $M$ of finite length and finite projective dimension such that $\ell\ell(M)$, the Lowey length of $M$, is equal to $\lambda(M)$, the length of $M$. background 0.70 0.16 0.03 asserted 0.53
s2 Then we show that necessarily $A$ is at worst a hypersurface singularity. result 1.00 0.92 0.83 asserted 1.00
s3 We also characterize Gorenstein local rings having a non-zero module $M$ of finite length and finite projective dimension with $\ell\ell(M) = \lambda(M)-1$. result 0.62 0.91 0.09 asserted 1.00

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 $(A,\mathfrak{m})$ be a Gorenstein local ring of dimension $d \geq 1$. Suppose there exists be a non-zero $A$ module $M$ of finite length and finite projective dimension such that $\ell\ell(M)$, the Lowey length of $M$, is equal to $\lambda(M)$, the length of $M$. Then we show that necessarily $A$ is at worst a hypersurface singularity. We also characterize Gorenstein local rings having a non-zero module $M$ of finite length and finite projective dimension with $\ell\ell(M) = \lambda(M)-1$.

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