Almost Noetherian rings and modules

Xiaolei Zhang

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arXiv · 2509.05996

Almost Noetherian rings and modules

Xiaolei Zhang

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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 \cite[9, B. Zavyalov, {\it Almost coherent modules and almost coherent sheaves}, Memoirs of the European Mathematical Society 19. Berlin: European Mathematical Society (EMS), 2025] under a certain condition.

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Xiaolei Zhang. 2025-09-07. Almost Noetherian rings and modules. https://arxiv.org/abs/2509.05996

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