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Integer-Valued Polynomials: Looking for Regular Bases (A Survey)

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Commutative Algebra

Abstract

This paper reviews recent results about the additive structure of algebras of integer-valued polynomials and, particularly, the question of the existence and the construction of regular bases. Doing this, we will be led to consider questions of combinatorial, arithmetical, algebraic, ultrametric, or dynamical nature.

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Acknowledgements

The author thanks the anonymous referee for many valuable suggestions.

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Authors and Affiliations

  1. LAMFA CNRS-UMR 7352, Université de Picardie, 33 rue Saint Leu, 80039, Amiens, France

    Jean-Luc Chabert

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  1. Jean-Luc Chabert
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Correspondence to Jean-Luc Chabert .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  2. Department of Mathematics, Graz University of Technology, Graz, Austria

    Sophie Frisch

  3. Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA

    Sarah Glaz

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Chabert, JL. (2014). Integer-Valued Polynomials: Looking for Regular Bases (A Survey). In: Fontana, M., Frisch, S., Glaz, S. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0925-4_5

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