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Integer-valued polynomials on algebras: a survey
Sophie Frisch1
1 Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 27-32.

We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.

Published online:
DOI: 10.5802/acirm.30
Classification: 13F20, 13F05, 13B25, 13J10, 11C08, 11C20
Keywords: Integer-valued polynomials, matrices, quaternions, group rings, Prüfer domains.
Sophie Frisch 1

1 Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria 
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Sophie Frisch. Integer-valued polynomials on algebras:  a survey. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 27-32. doi : 10.5802/acirm.30. https://acirm.centre-mersenne.org/articles/10.5802/acirm.30/

[1] P.-J. Cahen and J.-L. Chabert, Integer-Valued Polynomials, Math. Surveys and Monographs 48, Amer. Math. Soc., Povidence, R.I., 1997.

[2] S. Frisch, Polynomial separation of points in algebras, in Arithmetical Properties of Commutative Rings and Monoids, 253–259, Lect. Notes Pure Appl. Math. 241, Chapman & Hall, Boca Raton, 2005. | Zbl

[3] S. Frisch, Integer-valued polynomials in algebra, preprint. | DOI | MR

[4] F. Halter-Koch and W. Narkiewicz, Commutative rings and binomial coefficients, Monatsh. Math. 114 (1992), 107–110. | DOI | Zbl

[5] K. A. Loper, A generalization of integer-valued polynomial rings, preprint. | DOI | MR | Zbl

[6] N. Werner, Integer-valued polynomials over quaternions rings, J. Algebra 324 (2010), 1754–1769. | DOI | Zbl

[7] N. Werner, Integer-valued polynomials over matrix rings, Comm. Algebra, to appear. | DOI | MR | Zbl

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