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August 23, 2025International Mathematics Research Notices0 citations

Uniformity in Nonreduced Rings via Noetherian Operators

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YCYairon Cid‐RuizJJJack Jeffries

Key Points

  • Several uniformity results were obtained for nonreduced rings, enhancing the understanding of their structure.
  • The study introduces a differential version of the artin-rees lemma, crucial for applications in algebra.
  • Employing noetherian differential operators facilitated new insights into ring uniformity and operability.
  • This research indicates that further exploration in nonreduced rings may yield even broader algebraic implications.

Abstract

Abstract We prove a differential version of the Artin–Rees lemma with the use of Noetherian differential operators. As a consequence, we obtain several uniformity results for nonreduced rings.

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Cite This Study

Cid‐Ruiz et al. (2025) studied this question.

synapsesocial.com/papers/68af570dad7bf08b1eaddd8ehttps://doi.org/10.1093/imrn/rnaf260
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Uniformity in nonreduced rings via Noetherian operators2024
  2. 2Rings whose subrings are all Noetherian or Artinian2024
  3. 3Algebraic Variant of Noether Operator Theory2025
  4. 4Some Special Perfect c-Nonlinear Functions on ℤn2024
  5. 5Artinian rings which are not generalized Rickart2024