Results 31 to 40 of about 99,592 (142)
Integral closure of rings of integer-valued polynomials on algebras
, 2014 Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e.
G. Peruginelli +10 more
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Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power [PDF]
, 2010 We characterize the fixed divisor of a polynomial $f(X)$ in $\mathbb{Z}[X]$ by looking at the contraction of the powers of the maximal ideals of the overring ${\rm Int}(\mathbb{Z})$ containing $f(X)$. Given a prime $p$ and a positive integer $n$, we also
Giulio Peruginelli +14 more
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Interpolation by Integer-Valued Polynomials
Journal of Algebra, 1999 The author pursues two directions to construct interpolating integer-valued polynomials on Krull domains \(R\), that means, given distinct \(a_1, \dots, a_n\in S\leq R\) and \(b_1, \dots, b_n\in R\) there exists an \(f\in \text{Int}(S,R)= \{f\in K[x] \mid f(S)\subseteq R\}\), \(K\) being the quotient field of \(R\), with \(f(a_i) =b_i\), \(i=1, \dots,n\
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Positive exponential sums and odd polynomials [PDF]
, 2013 Given an odd integer polynomial f(x) of a degree k >=3, we construct a non-negative valued, normed trigonometric polynomial with the spectrum in the set of integer values of f(x) not greater than n, and a small free coefficient a_{0}=O((\log n)^{-1/k ...
Nincevic, Marina, Slijepcevic, Sinisa
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.121221222 . . . Is Not Quadratic [PDF]
, 2005 In this note, we show that if b > 1 is an integer, f(X) 2 Q[X] is an integer valued quadratic polynomial and K > 0 is any constant, then the b-adic number(...) where an 2 Z and 1 |an| K for all n 0, is neither rational nor ...
Luca, Florian
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Pr\"ufer intersection of valuation domains of a field of rational functions [PDF]
, 2018 Let $V$ be a rank one valuation domain with quotient field $K$. We characterize the subsets $S$ of $V$ for which the ring of integer-valued polynomials ${\rm Int}(S,V)=\{f\in K[X] \mid f(S)\subseteq V\}$ is a Pr\"ufer domain.
Peruginelli, Giulio
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Integer-valued polynomials over quaternion rings
Journal of Algebra, 2010 Let \(R=\mathbb ZQ\) be the ring of quaternions with integer coefficients. Then its division ring of fractions is equal to \(D=\mathbb Q\otimes_{\mathbb Z}R\). Denote by \(\text{Int\,}R\) the ring of all polynomials \(f\) with coefficients in \(D\) such that \(f(R)\subseteq R\). For each positive integer \(n\) denote by \(I_n\) the ideal of polynomials
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Integer-valued polynomials, Prüfer domains, and localization [PDF]
Proceedings of the American Mathematical Society, 1993 Let A A be an integral domain with quotient field K K and let Int ( A ) \operatorname {Int} (A) be the ring of integer-valued polynomials on A : { P ∈ K [ X ] | P (
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Irreducibility of integer-valued polynomials I [PDF]
Communications in Algebra, 2020 Accepted for publication in Communications in ...
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Split Primes and Integer-Valued Polynomials
Journal of Number Theory, 1993 Let \(R\) be a Dedekind domain with finite residue fields, \(K\) its field of fractions, and denote by \(I\) the ring of integer-valued polynomials over \(R\), \(I=\{g(x)\in K[x];\;g(R)\subseteq R\}\). Let \(L\) be a finite separable extension of \(K\) and \(S\) be the integral closure of \(R\) in \(L\). For a nonzero prime ideal \(P\) of \(S\) write \(
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