Results 21 to 30 of about 431 (234)
Coding with skew polynomial rings
Journal of Symbolic Computation, 2009 The authors generalize the \(\theta\)-cyclic code defined by \textit{D. Boucher, W. Geiselmann} and \textit{F. Ulmer} [Appl. Algebra Eng. Commun. Comput. 18, No. 4, 379--389 (2007; Zbl 1159.94390)] and study their properties. These are closely related to properties of the ring \(\mathbb{F}_q[X, \theta]\) of skew polynomials [see \textit{B. R. McDonald},
Boucher, Delphine, Ulmer, Félix
openaire +3 more sources
ON COEFFICIENTS OF NILPOTENT POLYNOMIALS IN SKEW POLYNOMIAL RINGS [PDF]
Korean Journal of Mathematics, 2013 Summary: We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of \(\alpha \)-skew \(n\)-semi-Armendariz ring, where \(\alpha\) is a ring endomorphism. We prove that a ring
Nam, Sang Bok +2 more
openaire +1 more source
Nilpotent Elements in Skew Polynomial Rings [PDF]
Journal of Sciences, Islamic Republic of Iran, 2017 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings.
M. Azimi, A. Moussavi
doaj
Prime ideals of skew polynomial rings and skew Laurent polynomial rings
Mathematical Journal of Okayama University, 1990 Let \(S=R[X,X^{-1};\rho]\) be a skew Laurent polynomial ring over a ring \(R\) with automorphism \(\rho\). The authors characterize those prime ideals \(P\) of \(S\) with \(P\cap R=0\) in terms of irreducible polynomials over the centre of \(Q[X,X^{-1};\rho]\), where \(Q\) is the right Martindale quotient of \(R\) with respect to the filter of non-zero
Cisneros, Eduardo +2 more
openaire +4 more sources
Generalized Skew Polynomial Rings [PDF]
Transactions of the American Mathematical Society, 1982 For a totally ordered cancellative semigroup Γ \Gamma
openaire +1 more source
Quasi-duo skew polynomial rings
Journal of Pure and Applied Algebra, 2008 A characterization of right (left) quasi-duo skew polynomial rings of endomorphism type and skew Laurent polynomial rings are given. In particular, it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is commutative modulo its Jacobson radical iff R[x] is left quasi-duo, (2) the skew Laurent polynomial ring is right quasi-duo iff ...
Leroy, André +2 more
openaire +3 more sources
Computation of nonlinear eigenvalues based on the Ore determinant: preliminary results [PDF]
Proceedings of the Estonian Academy of SciencesThe concept of eigenvalues has recently been generalized for nonlinear systems, but the method to find them is missing. Unlike the linear case, now one has to deal with non-commutative polynomials from the Ore ring. In the paper, the Ore determinant of a
Miroslav Halás +3 more
doaj +1 more source
Semifields from skew polynomial rings [PDF]
advg, 2013 Abstract Skew polynomial rings are used to construct finite semifields, following from a construction of Ore and Jacobson of associative division algebras. Johnson and Jha [10] constructed the so-called cyclic semifields, obtained using irreducible semilinear transformations.
LAVRAUW, MICHEL, SHEEKEY, JOHN FRANCIS
openaire +3 more sources
Angewandte Chemie, EarlyView.Color‐pure all‐organic emitters, i.e., with narrow spectral characteristics, are intensively studied for high‐definition organic LEDs and multi‐color bioimaging. In order to guide targeted materials design, this educative review discusses spectral characteristics, proper definitions and units, and the physical basis of spectral broadening, to distill ...
Johannes Gierschner +6 more
wiley +2 more sources
Uniserial Rings and Skew Polynomial Rings
Tokyo Journal of Mathematics, 1984 If \(\tau\) is an automorphism of a division ring D then, for each positive integer c, the factor ring \(S/x^ cS\) of the skew polynomial ring \(S=D[x;\tau]\) is a local uniserial ring of split type. The purpose of this paper is to establish a necessary and sufficient condition on a local uniserial ring R for R to be isomorphic to a ring of the above ...
openaire +3 more sources