Results 1 to 10 of about 288 (227)
Radicals of skew polynomial rings and skew Laurent polynomial rings
Journal of Algebra, 2011 In this paper, \(R\) denotes an associative ring with identity, and \(\sigma\) stands for an automorphism of \(R\). \(W(R)\), \(L(R)\) and \(N(R)\) denote the Wedderburn radical, the Levitzki radical and the upper nil radical of \(R\), respectively. An ideal \(I\) of \(R\) is called a \(\sigma\)-ideal if \(\sigma(I)\subseteq I\).
, Yang Lee
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Coding with skew polynomial rings
Journal of Symbolic Computation, 2009 The authors generalize the \(\theta\)-cyclic code defined by \textit{D. Boucher, W. Geiselmann} and \textit{F. Ulmer} [Appl. Algebra Eng. Commun. Comput. 18, No. 4, 379--389 (2007; Zbl 1159.94390)] and study their properties. These are closely related to properties of the ring \(\mathbb{F}_q[X, \theta]\) of skew polynomials [see \textit{B. R. McDonald},
Delphine Boucher, Felix Ulmer
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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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Skew Polynomial Rings: the Schreier Technique [PDF]
Acta Mathematica Vietnamica, 2022 AbstractSchreier bases are introduced and used to show that skew polynomial rings are free ideal rings, i.e., rings whose one-sided ideals are free of unique rank, as well as to compute a rank of one-sided ideals together with a description of corresponding bases. The latter fact, a so-called Schreier-Lewin formula (Lewin Trans. Am. Math.
Pham Ngoc Anh
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On Nilpotent Elements of Skew Polynomial Rings
Journal of Mathematical Extension, 2012 We study the structure of the set of nilpotent elements in skew polynomial ring R[x; α], when R is an α-Armendariz ring. We prove that if R is a nil α-Armendariz ring and α t = IR, then the set of nilpotent elements of R is an α-compatible subrng of ...
J. Esmaeili, E. Hashemi
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Endo-Noetherian Skew Generalized Power Series Rings [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2023 Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian.
Ramy Abdel-Khaleq +2 more
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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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Some interactions between Hopf Galois extensions and noncommutative rings
Universitas Scientiarum, 2022 In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW ...
Armando Reyes, Fabio Calderón
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Linear codes and cyclic codes over finite rings and their generalizations: a survey
Electronic Journal of Graph Theory and Applications, 2023 We survey a recent progress of cyclic codes over finite rings and their generalization to skew cyclic as well as skew cyclic codes with derivation over finite rings, focusing on structural properties of the codes.
Djoko Suprijanto
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The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems
Eng, 2021 A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters.
Edward W. Kamen
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