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Noetherian-like properties and zero-dimensionality in some extensions of rings

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This paper investigates the transfer of the locally Noetherian property to flat overrings, Serre and Nagata rings, trivial ring extensions, the finite direct product of rings, and amalgamated duplications. We also study the transfer of the Q-Noetherian property to the Nagata ring and amalgamated duplications, and we provide an analog of the Eakin–Nagata theorem. We define the locally Q-Noetherian property and study its transfer to flat overrings, the finite direct product of rings, the Nagata ring, trivial ring extensions, and amalgamated duplications. We also introduce the notion of the Q-Artinian ring and prove that this class of rings coincides with 0-dimensional rings. Special attention is given to the study of Q-strongly 0-dimensional rings.

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Acknowledgements

The authors sincerely thank the reviewers for their careful reading and suggestions. The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2021R1I1A3047469).

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Authors and Affiliations

  1. Division of Computer Engineering, Hoseo University, Asan, 31499, Republic of Korea

    Hwankoo Kim

  2. Science and Technology Research Laboratory (LRST), The Higher School of Education and Training, Ibn Zohr University, Agadir, Morocco

    Omar Ouzzaouit

  3. Department of Mathematics, The Regional Center for Education and Training Professions Souss Massa, Inezgane, Morocco

    Ali Tamoussit

  4. Laboratory of Mathematics and Applications (LMA), Faculty of Sciences, Ibn Zohr University, Agadir, Morocco

    Ali Tamoussit

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  1. Hwankoo Kim
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  2. Omar Ouzzaouit
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Correspondence to Hwankoo Kim.

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Kim, H., Ouzzaouit, O. & Tamoussit, A. Noetherian-like properties and zero-dimensionality in some extensions of rings. Afr. Mat. 34, 42 (2023). https://doi.org/10.1007/s13370-023-01083-3

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