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Ring–theoretic properties of locally Mori domains and rings of the form \(\mathrm {Int}(E,D)\)

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Abstract

An integral domain D is said to be locally Mori if any localization of D at a maximal ideal is a Mori domain. In this paper we are concerned with some ring–theoretic properties of locally Mori domains and their rings of integer-valued polynomials. First, we present some results on the transfer of the locally Mori property to flat overrings, Nagata ideal transforms, polynomial ring extensions and pullback constructions. Then, we investigate rings of integer-valued polynomials over (locally) Mori domains, and for an integral domain D,  we give a necessary condition for \(\mathrm {Int}(D)\) to be an \(\mathrm {MZ}\)-Mori domain.

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Acknowledgements

We would like to express our sincere thanks to the referee for his/her rich, fruitful and detailed comments that have greatly improved the paper.

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Author notes

  1. Omar Ouzzaouit and Ali Tamoussit have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, The Higher School of Education and Training, Ibn Zohr University, 80000, Agadir, Morocco

    Omar Ouzzaouit

  2. Department of Mathematics, The Regional Center for Education and Training Professions Souss Massa, 80000, Inezgane, Morocco

    Ali Tamoussit

Authors
  1. Omar Ouzzaouit
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  2. Ali Tamoussit
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Correspondence to Omar Ouzzaouit.

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Communicated by Sergio R. López-Permouth.

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Ouzzaouit, O., Tamoussit, A. Ring–theoretic properties of locally Mori domains and rings of the form \(\mathrm {Int}(E,D)\). São Paulo J. Math. Sci. 17, 817–830 (2023). https://doi.org/10.1007/s40863-022-00304-0

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  • DOI: https://doi.org/10.1007/s40863-022-00304-0

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