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Proceedings of the American Mathematical Society, 1970 For aii algebra R over a field k, with residue field K to be a ring of polyniomials in one variable over k it is necessary that trdeg K/k = 1. We prove that under the hypothesis tr* deg K/k -1, R is a ring of Krtull-dimension at most one. This is used to derive sufficient conditions for R to be a ring of polynomials in one variable over k. 1.
Evyatar, A., Zaks, A.
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An immanant formulation of the dual canonical basis of the quantum polynomial ring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings.
Mark Skandera, Justin Lambright
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Integer-valued polynomials and binomially Noetherian rings
Zanco Journal of Pure and Applied Sciences, 2022 for each and i ≥ 0. The polynomial ring of integer-valued in rational polynomial is defined by Int ( an important example for binomial ring and is non-Noetherian ring. In this paper the algebraic structure of binomial rings has been studied by their
Shadman Kareem
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Ideals with linear quotients in Segre products [PDF]
Opuscula Mathematica, 2017 We establish that the Segre product between a polynomial ring on a field \(K\) in \(m\) variables and the second squarefree Veronese subalgebra of a polynomial ring on \(K\) in \(n\) variables has the intersection degree equal to three.
Gioia Failla
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Construction of Complex Lattice Codes via Cyclotomic Fields
Trends in Computational and Applied Mathematics, 2022 Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized ...
E. D. Carvalho +3 more
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Some results on counting roots of polynomials and the Sylvester resultant. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials.
Michael Monagan, Baris Tuncer
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LINEAR CODE THROUGH POLYNOMIAL MODULO Z [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2012 A polynomial p(x)= a + a x + …+ a x is said to be a permutation polynomial over a finite ring R If P permute the elements of R . where R is the ring ( Z , + , ) .
MAKARIM ABDULWAHIDE
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BEBERAPA SIFAT IDEAL GELANGGANG POLINOM MIRING: SUATU KAJIAN PUSTAKA
Jurnal Matematika, 2012 Let R be a ring with identity 1 and s be an endomorphism of R and d be a left s - derivation . The skew polynomial ring over R in an indeterminate x is: R[x;s ,d ] = { f (x) = anxn +L+ a0 | ai Î R} with xa =s (a)x +d (a) The aim of this research is to ...
AMIR KAMAL AMIR
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Apolarity, Hessian and Macaulay polynomials [PDF]
, 2012 A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b.
Alexander J. +12 more
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The Structure of Local Rings with Singleton Basis and Their Enumeration
Mathematics, 2022 A local ring is an associative ring with unique maximal ideal. We associate with each Artinian local ring with singleton basis four invariants (positive integers) p,n,s,t.
Yousef Alkhamees, Sami Alabiad
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