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Various properties of a general class of integer-valued polynomials

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Abstract

In this paper, we study various properties for some classes of domains that are generalizations of integer-valued polynomial rings. For D an integral domain with quotient field K and E a subset of K, one defines as usual \(\mathrm {Int}(E,D):=\{f\in K[X]:\;f(E)\subseteq D\}.\) If R is an integral domain containing D, then we define \(\mathrm {Int}_R(E,D):=\{f\in R[X]:\;f(E)\subseteq D\},\) which is called the ring of D-valued R-polynomials over E. Among other things, we investigate various properties and facts around the rings \(\mathrm {Int}_R(E,D)\), such as localization, (faithful) flatness, Krull dimension and some other transfer properties.

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Acknowledgements

The authors would like to thank the referee for careful reading and correcting a couple of errors which substantially improved this article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdallah, Fez, Morocco

    Mohamed Mahmoud Chems-Eddin

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

    Ali Tamoussit

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  1. Mohamed Mahmoud Chems-Eddin
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  2. Ali Tamoussit
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Chems-Eddin, M.M., Tamoussit, A. Various properties of a general class of integer-valued polynomials. Beitr Algebra Geom 64, 81–93 (2023). https://doi.org/10.1007/s13366-021-00619-7

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