Results 11 to 20 of about 59,541 (246)
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.
europepmc +2 more sources
Quantitative bounds for the $U^4$-inverse theorem over low characteristic finite fields
Discrete Analysis, 2022 Quantitative bounds for the $U^4$-inverse theorem over low characteristic finite fields, Discrete Analysis 2022:14, 17 pp. Let $G$ be a finite Abelian group and let $f$ be a complex-valued function defined on $G$.
Jonathan Tidor
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Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
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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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