Results 11 to 20 of about 1,801,897 (347)
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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Generalized Weyl algebras and diskew polynomial rings [PDF]
Journal of Algebra and its Applications, 2020 The aim of the paper is to extend the class of generalized Weyl algebras (GWAs) to a larger class of rings (they are also called GWAs) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ GWAs.
Bavula, V.V.
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Differential polynomial rings over rings satisfying a polynomial identity [PDF]
Journal of Algebra, 2014 Let R be a ring satisfying a polynomial identity and let δ be a derivation of R. We show that if R is locally nilpotent then R[x;δ] is locally nilpotent. This affirmatively answers a question of Smoktunowicz and Ziembowski.
J. Bell, Blake Madill, Forte Shinko
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Indagationes Mathematicae (Proceedings), 1968 Skew polynomial rings .are considered with a multiplication defined byx•a=a1x+a1x2+…+arxr,ai∈K,where K is a (skew) field and the ai depend on a ∈ K.
Smits, T.H.M.
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Polynomial identity rings as rings of functions
Journal of Algebra, 2007 We generalize the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative setting, where “varieties” carry a PGLn-action, regular and rational ...
Vonessen, N., Reichstein, Z.
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Algorithmic Properties of Polynomial Rings
Journal of Symbolic Computation, 1998 In this paper we investigate how algorithms for computing heights, radicals, unmixed and primary decompositions of ideals can be lifted from a Noetherian commutative ringRto polynomial rings ...
KALKBRENER, M.
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On the Waring problem for polynomial rings. [PDF]
Proc Natl Acad Sci U S A, 2012 In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k ≥2 can be represented as a sum of at most k
Fröberg R, Ottaviani G, Shapiro B.
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The Regularity Conjecture for prime ideals in polynomial rings
EMS Surveys in Mathematical Sciences, 2021 This paper presents a survey on recent developments on regularity of prime ideals in polynomial rings.
J. McCullough, I. Peeva
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Ring-LWE in Polynomial Rings [PDF]
IACR Cryptology ePrint Archive, 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,
L. Ducas, A. Durmus
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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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