Integer valued polynomials - Open Access .click

Monatshefte für Mathematik, 2013
Let \(D\) be an integral domain with quotient field \(K\), and denote by \(T_n(D)\) the set of \(n\)-dimensional lower triangular matrices with entries from \(D\). The authors study the set \(\mathrm{Int}(T_n(D))\) of integer valued polynomials, i.e. polynomials \(f\in K(x)\) satisfying \(f(T_n(D))\subset T_n(D)\). First they consider the case \(D=Z\),
Evrard, S., Fares, Y., Johnson, K.
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Algebraic-integer valued polynomials

Journal of Number Theory, 2022
Let \(R\) be a Dedekind domain of a global field \(K\). Let \(\mathrm{int}(n,R):=\{\alpha\in\overline{R}\mid [K(\alpha):K]=n\}\) and \(\mathrm{int}(\leq n,R):=\{\alpha\in\overline{R}\mid [K(\alpha):K]\leq n\}\). The main object of study of this paper is the ring \(\mathrm{Int}_K(E,\overline{R})\), that is the set of \(m\)-variate polynomials \(f\in K ...
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Integer-valued skew polynomials

Journal of Algebra and Its Applications, 2020
For a commutative integral domain [Formula: see text] with field of fractions [Formula: see text], the ring of integer-valued polynomials on [Formula: see text] is [Formula: see text]. In this paper, we extend this construction to skew polynomial rings. Given an automorphism [Formula: see text] of [Formula: see text], the skew polynomial ring [Formula:
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Value-sets of polynomials at p-adic integers

Mathematische Zeitschrift, 2011
Let \({\mathbb Z}_p\) be the ring of \(p\)-adic integers. The objective of this paper is to study the classification of subsets of \({\mathbb Z}_p\) which are images \(f({\mathbb Z}_p^r)\) of polynomial functions \(f: {\mathbb Z}_p^r\to {\mathbb Z}_p\) with \(f\in {\mathbb Q}_p[X_1,\ldots,X_r]\) and with \(f\in{\mathbb Z}_p [X_1,\ldots,X_r]\).
DVORNICICH, ROBERTO, Zannier U.
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integer-valued polynomials
algebra and number theory
polynomials over commutative rings

polynomials in number theory
integer-valued polynomial
fos: mathematics

mathematics
polynomials irreducibility, etc.
integral domains