Almost Noetherian rings and modules
Commutative Algebra
2026-02-24 v2
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.
Keywords
Cite
@article{arxiv.2509.05996,
title = {Almost Noetherian rings and modules},
author = {Xiaolei Zhang},
journal= {arXiv preprint arXiv:2509.05996},
year = {2026}
}