Results 191 to 200 of about 288 (227)

The McCoy Condition on Skew Polynomial Rings

Communications in Algebra, 2009
Based on a theorem of McCoy on commutative rings, Nielsen called a ring R right McCoy if, for any nonzero polynomials f(x), g(x) over R, f(x)g(x) = 0 implies f(x)r = 0 for some 0 ≠ r ∊ R. In this note, we consider a skew version of these rings, called σ-skew McCoy rings, with respect to a ring endomorphism σ.
Muhittin Baser, Tai Keun Kwak, Yang Lee   +2 more
exaly   +3 more sources

Radicals in skew polynomial and skew Laurent polynomial rings

Journal of Pure and Applied Algebra, 2014
It is well known that classical radicals and some radical-like ideals of skew polynomial and skew Laurent polynomial rings are determined in a regular way by specified ideals of the coefficient ring. However, a detailed description of these coefficient ideals is far from easy.
Hong, Chan Yong, Kim, Nam Kyun, Nielsen, Pace P.   +2 more
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Kötter interpolation in skew polynomial rings

Designs, Codes and Cryptography, 2013
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Siyu Liu 0007, Felice Manganiello, Frank R. Kschischang   +2 more
openaire   +1 more source

Bezout rings and skew polynomials

Russian Mathematical Surveys, 2001
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Primitivity of skew polynomial and skew laurent polynomial rings

Communications in Algebra, 1996
Let R be a noetherian P.I. ring and S an automorphism of R. Necessary and sufficient conditions for the primitivity of the skew Laurent polynomial ring R[t;t-1S] and the skew polynomial ring R[t,S] are given.
André Leroy, Jerzy Matczuk
openaire   +1 more source

Radicals of skew polynomial rings and skew Laurent polynomial rings

Mathematical Journal of Okayama University, 1987
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.
openaire   +3 more sources

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].
openaire   +1 more source

Extended Centroids of Skew Polynomial Rings

Canadian Mathematical Bulletin, 1985
AbstractLet R be a prime ring with σ ∊ Aut (R). We determine the extended centroid of the skew polynomial ring R[x, σ] when (i) 〈σ〉 is X-outer of finite order, (ii) 〈σ〉 is X-outer and infinite, (iii) σm is X-inner and no smaller power of σ fixes the extended centroid of R.
Rosen, Jerry D., Rosen, Mary Peles
openaire   +1 more source

Factoring in skew-polynomial rings

2005
Efficient algorithms are presented for factoring polynomials in the skew-polynomial ring K[x; σ], a non-commutative generalization of the usual ring of polynomials K[x], where K is a finite field and σ: K → K is an automorphism. Applications include fast functional decomposition algorithms for a class of polynomials in K[x] whose decompositions are ...
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Real Valuations on Skew Polynomial Rings

Algebras and Representation Theory, 2013
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Granja, Ángel, Martínez, Ma. Carmen, Rodríguez, Cristina   +2 more
openaire   +2 more sources