Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions

Nicholas J. Werner ()
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Nicholas J. Werner: SUNY College at Old Westbury, Department of Mathematics, Computer and Information Science

A chapter in Rings, Polynomials, and Modules, 2017, pp 353-375 from Springer

Abstract: Abstract Given a commutative integral domain D with fraction field K, the ring of integer-valued polynomials on D is Int(D) = {f ∈ K[x]∣f(D) ⊆ D}. In recent years, attention has turned to generalizations of Int(D) where the polynomials act on D-algebras rather than on D itself. We survey the present activity on this topic and propose questions for further research.

Keywords: Integer-valued polynomial; Algebra; P-ordering; Regular basis; Int-decomposable; Integral closure; Prüfer domain; Matrix; Quaternion; Octonion; Integer-valued rational function; Primary 13F20; 16S36; Secondary 13F05; 13B22; 11R52; 11C99; 17D99 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_18

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DOI: 10.1007/978-3-319-65874-2_18

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