Results 1 to 10 of about 431 (234)
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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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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Zero-divisor graphs of twisted partial skew generalized power series rings [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. Design/methodology/approach
Mohammed H. Fahmy +2 more
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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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A dual approach to structure constants for K-theory of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants
Huilan Li, Jennifer Morse, Pat Shields
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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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Irreducible skew polynomials over domains
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ -derivation. We give criteria for skew polynomials f ∈ R of degree less or equal to four to be irreducible.
Brown C., Pumplün S.
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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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Galois groups over rational function fields over skew fields
Comptes Rendus. Mathématique, 2020 Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.
Alon, Gil +2 more
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Ingeniería y Ciencia, 2020 In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew ...
Armando Reyes +1 more
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