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Integer-valued polynomials on algebras: a survey. (English) Zbl 1474.13044

Summary: 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.

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13B25 Polynomials over commutative rings
13J10 Complete rings, completion
11C08 Polynomials in number theory
11C20 Matrices, determinants in number theory

References:

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[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 1092.13027
[3] S. Frisch, Integer-valued polynomials in algebra, preprint. · Zbl 1273.13037
[4] F. Halter-Koch and W. Narkiewicz, Commutative rings and binomial coefficients, \(Monatsh. Math.\)114 (1992), 107-110. · Zbl 0764.12002
[5] K. A. Loper, A generalization of integer-valued polynomial rings, preprint. · Zbl 0896.13015
[6] N. Werner, Integer-valued polynomials over quaternions rings, \(J. Algebra\)324 (2010), 1754-1769. · Zbl 1219.16027
[7] N. Werner, Integer-valued polynomials over matrix rings, \(Comm. Algebra\), to appear. Copyright Cellule MathDoc 2018
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