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October 12, 20250 citationsOpen Access

Almost Noetherian rings and modules

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XZXiaolei Zhang

Key Points

  • The study introduces various theorems related to almost noetherian rings, offering deep insights.
  • Key theorems discussed include Cohen type and Hilbert basis theorems, which enhance understanding of ring structures.
  • The paper resolves an important question previously raised about almost noetherian rings, contributing to the field's knowledge.
  • Constructs of rings derived from almost noetherian properties are explored, enhancing the landscape of ring theory.

Abstract

In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for almost Noetherian rings. In particular, we resolve a question proposed in 8.

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Cite This Study

Xiaolei Zhang (2025) studied this question.

synapsesocial.com/papers/68ec1be02b8fa9b2b78ad1a3https://doi.org/10.48550/arxiv.2509.05996
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