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On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings

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Abstract

The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Small group Research Project under grant number RGP1/276/44.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box. 9004, Abha, Saudi Arabia

    Khaled Alhazmy & Fuad Ali Ahmed Almahdi

  2. Modelling and Mathematical Structures Laboratory, Department of Mathematics, Faculty of Science and Technology of Fez, University S.M. Ben Abdellah Fez, Box 2202, Fes, Morocco

    Younes El Haddaoui & Najib Mahdou

Authors
  1. Khaled Alhazmy
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  2. Fuad Ali Ahmed Almahdi
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  3. Younes El Haddaoui
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  4. Najib Mahdou
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Correspondence to Najib Mahdou.

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Communicated by Rasool Hafezi.

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Alhazmy, K., Almahdi, F.A.A., El Haddaoui, Y. et al. On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings. Bull. Iran. Math. Soc. 50, 21 (2024). https://doi.org/10.1007/s41980-023-00856-7

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  • DOI: https://doi.org/10.1007/s41980-023-00856-7

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