Results 81 to 90 of about 3,780 (109)

Descriptions of radicals of skew polynomial and skew Laurent polynomial rings

Journal of Pure and Applied Algebra, 2019
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Hong, Chan Yong, Kim, Nam Kyun
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Distributive skew Laurent polynomial rings

Journal of Mathematical Sciences, 2012
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McCOY PROPERTY OF SKEW LAURENT POLYNOMIALS AND POWER SERIES RINGS

Journal of Algebra and Its Applications, 2013
One of the important properties of commutative rings, proved by McCoy [Remarks on divisors of zero, Amer. Math. Monthly49(5) (1942) 286–295], is that if two nonzero polynomials annihilate each other over a commutative ring then each polynomial has a nonzero annihilator in the base ring.
Alhevaz, A., Kiani, D.
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Radicals of Skew Polynomial and Skew Laurent Polynomial Rings Over Skew Armendariz Rings

Communications in Algebra, 2013
In this note we study radicals of skew polynomial ring R[x; α] and skew Laurent polynomial ring R[x, x −1; α], for a skew-Armendariz ring R. In particular, among the other results, we show that for an skew-Armendariz ring R, J(R[x; α]) = N 0(R[x; α]) = Nil*(R)[x; α] and J(R[x, x −1; α]) = N 0(R[x, x −1; α]) = Nil*(R)[x, x −1; α].
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K₁of Corner Skew Laurent Polynomial Rings and Applications

Communications in Algebra, 2005
ABSTRACT We give a description of the Whitehead group of a corner skew Laurent polynomial ring A[t +, t −; α] associated with an isomorphism α: A → pAp from a unital associative ring A onto a corner ring pAp. Using this, we compute the Whitehead group of the Leavitt algebras of type (1, n).
Pere Ara, Miquel Brustenga
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On diameter of the zero-divisor and the compressed zero-divisor graphs of skew Laurent polynomial rings

Journal of Algebra and Its Applications, 2019
Let [Formula: see text] be an associative ring with nonzero identity. The zero-divisor graph [Formula: see text] of [Formula: see text] is the (undirected) graph with vertices the nonzero zero-divisors of [Formula: see text], and distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] or [Formula ...
Hashemi, Ebrahim, Abdi, Mona, Alhevaz, Abdollah   +2 more
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On skew Laurent polynomial rings over locally nilpotent rings

Linear Algebra and its Applications, 2018
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Prime links in some skew-polynomial and skew-laurent rings

Communications in Algebra, 1997
Let R be a Noetherian commutative ring and a α1,…,αn commuting automorphisms of R. Define T = R[θ1,…,θn;α1,…,αn] to be the skew-polynomial ring with θir = αi(r)θi and θiθj= θjθi, for all i,j ∊ (1,…,n) and r ∊ R, and let S = Rθ1,θ1:-1,…,θn:,θn;-1;α1:,…,αn] be the corresponding skew-Laurent ring.
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Commutative subalgebras of the ring of quantum polynomials and of the skew field of quantum Laurent series

Sbornik: Mathematics, 2001
The author considers the quantum algebra \(\Lambda\) in \(n\) variables over a field \(k\) and its completion \(\mathcal F\), the skew field of quantum Laurent series. The lowest degree of any terms occurring defines a valuation \(\|.\|\) on \(\mathcal F\) with values in \(\mathbb{Z}^n\) and the author proves that if all elements commuting with \(f\in{\
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Radicals of skew polynomial rings and skew Laurent polynomial rings

2016
Let K be a ring, \(\rho\) an automorphism of K, and D a derivation of K. We denote by K[X;\(\rho\) ] (resp. \(K\), resp. K[X;D]) the skew polynomial ring of automorphism type (resp. skew Laurent polynomial ring; resp. skew polynomial ring of derivation type) over K. In [\textit{S. S. Bedi}, \textit{J. Ram}, Isr. J. Math.
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