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Polynomial Rings over Pseudovaluation Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x∉P for any P∈Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring.
V. K. Bhat
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Nilpotent graphs of skew polynomial rings over non-commutative rings [PDF]
Transactions on Combinatorics, 2020 Let $R$ be a ring and $\alpha$ be a ring endomorphism of $R$. The undirected nilpotent graph of $R$, denoted by $\Gamma_N(R)$, is a graph with vertex set $Z_N(R)^*$, and two distinct vertices $x$ and $y$ are connected by an edge if and only if ...
Mohammad Javad Nikmehr, Abdolreza Azadi
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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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The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography [PDF]
Mathematics Interdisciplinary Research, 2022 This survey illustrates and investigates the application of polynomial rings over finite fields to generate PRN codes for Global Navigation Satellite System (GNSS) satellites.
Amir Bagheri, Hassan Emami
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Lim Ulrich sequences and Boij-Söderberg cones
Forum of Mathematics, Sigma, 2023 This paper extends the results of Boij, Eisenbud, Erman, Schreyer and Söderberg on the structure of Betti cones of finitely generated graded modules and finite free complexes over polynomial rings, to all finitely generated graded rings admitting linear ...
Srikanth B. Iyengar +2 more
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Ring-LWE in Polynomial Rings [PDF]
, 2012 The Ring-LWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the Ring-LWE problem defined in [LPR10] involves the fractional ideal R ∨, the dual of the ring R , which is the source of many theoretical and implementation technicalities. Until now,
Ducas, Léo, Durmus, Alain
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Semihereditary polynomial rings [PDF]
Proceedings of the American Mathematical Society, 1974 It is shown that if the ring of polynomials over a commutative ring R R is semihereditary then R R is von Neumann regular. This is the converse of a theorem of P. J. McCarthy.
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An extension of the reflexive property of rings
Arab Journal of Mathematical Sciences, 2019 Mason introduced the notion of reflexive property of rings as a generalization of reduced rings. For a ring endomorphism α, Krempa studied α-rigid rings as an extension of reduced rings. In this note, we introduce the notion of α-quasi reflexive rings as
Arnab Bhattacharjee
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Jordan derivations of polynomial rings
Karpatsʹkì Matematičnì Publìkacìï, 2012 We study connections between the set of Jordan derivations of a ring $R$ and the sets of Jordan derivations of a polynomial ring $R[x_1,\dots,x_n]$ and formal power series ring $R[[x_1,\dots,x_n]]$. We also establish a condition when $JDer R$ is a left $
I. I. Lishchynsky
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A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
Open Mathematics, 2015 Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable ...
Zhao Xiangui, Zhang Yang
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