Results 11 to 20 of about 59,442 (147)
Integer-Valued Polynomials and Prüfer v-Multiplication Domains
Journal of Algebra, 2000 If \(D\) is a domain with quotient field \(K\) then the ring of integer valued polynomials over \(D\) is \(\text{Int}(D)=:\{f \in K[X] \mid f(D) \subseteq D\}\). This paper is devoted to relating certain properties of \(\text{Int}(D)\) to those of \(D\). A domain, \(D\), is Prüfer if for each prime ideal, \(P\), \(D_P\) is a valuation domain.
CAHEN P. J +2 more
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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
Nicholas J Werner
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Generalized rings of integer-valued polynomials
Journal of Number Theory, 2012 Let us first recall the definition of the classical ring of integer-valued polynomials \(\mathrm{Int}(\mathbb{Z})=\{f(X)\in\mathbb{Q}[X];f(\mathbb{Z})\) \(\subseteq \mathbb{Z}\}\). In the literature, many generalizations are done where elements of \(\mathbb{Q}[X]\) act on sets such as rings of algebraic integers or the ring \(M_n(\mathbb{Z})\) of \(n ...
Loper, K. Alan, Werner, Nicholas J.
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Integer-valued polynomials on algebras
Journal of Algebra, 2013 17 pages; a glitch in the published version (J.Algebra 373 (2013) 414-425) has been corrected in this post-preprint, namely, in Prop. 6.2 and Thm. 6.3, the assumption "zero Jacobson radical" needs to be replaced by the stronger assumption "intersection of maximal ideals of finite index is zero"
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A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator. [PDF]
Commun Algebra, 2020 Frisch S, Nakato S.
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Irreducible polynomials in Int(ℤ)
ITM Web of Conferences, 2018 In order to fully understand the factorization behavior of the ring Int(ℤ) = {f ∈ ℚ[x] | f (ℤ) ⊆ ℤ} of integer-valued polynomials on ℤ, it is crucial to identify the irreducible elements.
Antoniou Austin +2 more
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The ring of polynomials integral-valued over a finite set of integral elements [PDF]
, 2016 Let $D$ be an integral domain with quotient field $K$ and $\Omega$ a finite subset of $D$. McQuillan proved that the ring ${\rm Int}(\Omega,D)$ of polynomials in $K[X]$ which are integer-valued over $\Omega$, that is, $f\in K[X]$ such that $f(\Omega ...
Peruginelli, G.
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REMARKS ON k-FOLD INTEGER-VALUED POLYNOMIALS [PDF]
Bulletin of the Korean Mathematical Society, 2002 For \(k=1,2,\dots\) denote by \(S_k\) the set of all polynomials \(f\) with rational coefficients having the property that \(f\) and its derivatives \(f',f'',\dots,f^{(k)}\) are integer-valued at rational integers. A characterization of polynomials in \(S_1\) has been given by \textit{L. Carlitz} [Indag. Math.
Laohakosol, Vichian, Sripayap, Angkana
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Non-triviality conditions for integer-valued polynomial rings on algebras [PDF]
, 2016 Let $D$ be a commutative domain with field of fractions $K$ and let $A$ be a torsion-free $D$-algebra such that $A \cap K = D$. The ring of integer-valued polynomials on $A$ with coefficients in $K$ is $\Int_K(A) = \{f \in K[X] \mid f(A) \subseteq A ...
Peruginelli, Giulio +1 more
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Integer-valued polynomials and $K$-theory operations [PDF]
Proceedings of the American Mathematical Society, 2010 This paper is based on the first author's thesis [\(\lq\lq\)Additive unstable operations in complex \(K\)-theory and cobordism'', Ph.D. Thesis, University of Sheffield, 2008]. The authors provide a unifying framework encompassing recent examples obtained by several authors of rings of integer-valued polynomials over \({\mathbb Q}\), which arise as ...
Strong, M-J., Whitehouse, Sarah
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