Results 1 to 10 of about 2,476 (50)
REVERSIBLE SKEW LAURENT POLYNOMIAL RINGS AND DEFORMATIONS OF POISSON AUTOMORPHISMS [PDF]
Journal of Algebra and Its Applications, 2009 A skew Laurent polynomial ring S = R[x±1;α] is reversible if it has a reversing automorphism, that is, an automorphism θ of period 2 that transposes x and x-1 and restricts to an automorphism γ of R with γ = γ-1. We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the
Jordan, D.A., Sasom, N.
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Simplicity of non-associative skew Laurent polynomial rings
Proceedings of the Edinburgh Mathematical Society, 2023 AbstractWe introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Öinert.
Per Bäck, Johan Richter
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We first study connections between α-compatible ideals of R and related ideals of the skew Laurent polynomials ring R[x,x−1;α], where α is an automorphism of R.
E. Hashemi
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Cremmer-Gervais cluster structure on SLn. [PDF]
Proc Natl Acad Sci U S A, 2014 We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of
Gekhtman M, Shapiro M, Vainshtein A.
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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 \(\sigma(I)\subseteq I\).
Hong, Chan Yong +2 more
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CHARACTERIZATIONS OF ELEMENTS IN PRIME RADICALS OF SKEW POLYNOMIAL RINGS AND SKEW LAURENT POLYNOMIAL RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2011 We show that the -prime radical of a ring R is the set of all strongly -nilpotent elements in R, where is an automorphism of R. We observe some conditions under which the -prime radical of R coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (; 1 )- (semi)primeness of ...
Jeoung-Soo Cheon +3 more
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Primitive skew Laurent polynomial rings [PDF]
Glasgow Mathematical Journal, 1978 In [8] the author studied the question of the primitivity of an Ore extension R[x, δ], where δ is a derivation of the ring R. If a is an automorphism of R then it can be shown that R[x, α] is primitive if the following conditions are satisfied: (i) no power αsS ≥ 1, of α is inner; (ii) the only ideals of R invariant under α are 0 and R.
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PRIME RADICALS OF SKEW LAURENT POLYNOMIAL RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2005 Summary: Let \(R\) be a ring with an automorphism \(\sigma\). An ideal \(I\) of \(R\) is a `\(\sigma\)-ideal' of \(R\) if \(\sigma(I)=I\). A proper ideal \(P\) of \(R\) is a `\(\sigma\)-prime ideal' of \(R\) if \(P\) is a \(\sigma\)-ideal of \(R\) and for \(\sigma\)-ideals \(I\) and \(J\) of \(R\), \(IJ\subseteq P\) implies that \(I\subseteq P\) or \(J\
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A quadratic Poisson Gel'fand-Kirillov problem in prime characteristic [PDF]
, 2015 The quadratic Poisson Gel’fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is Poisson birationally equivalent to a Poisson affine space, i.e. to a polyno-mial algebra K[X1,..., Xn] with Poisson bracket defined by {Xi, Xj} =
Launois, Stephane, Lecoutre, Cesar
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Prime ideals in skew Laurent polynomial rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1993 Let R be a commutative ring and {σ1,…,σn} a set of commuting automorphisms of R. Let T = be the skew Laurent polynomial ring in n indeterminates over R and let be the Laurent polynomial ring in n central indeterminates over R. There is an isomorphism φ of right R-modules between T and S given by φ(θj) = xj.
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