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On Cohen-Macaulay rings of invariants

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Martin Lorenz, Jawahar Pathak

Commutative Algebra · Submitted 20 Dec 2000

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

The authors' main claim We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group.

how it is stated · asserted 0.61 read the record →

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arXiv IDmath/0012201 (version 1)
Pith ID2A3UDB6P, Pith's permanent record of this paper and its review
CitationJawahar Pathak, Martin Lorenz. "On Cohen-Macaulay rings of invariants." arXiv:math/0012201 (2000). https://pith.science/paper/2A3UDB6P
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,953 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras $k[\bbZ^n]$ via an action on $\bbZ^n$.

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 investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. contribution 0.99 0.87 0.13 asserted 0.61
s1 Our point of view is ring theoretic and not a priori tailored to a particular type of group action. method 0.75 0.50 0.03 asserted 0.99
s2 As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras $k[\bbZ^n]$ via an action on $\bbZ^n$. contribution 0.79 0.80 0.03 asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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 investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras $k[\bbZ^n]$ via an action on $\bbZ^n$.

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