Results 1 to 10 of about 2,498 (67)
Attached prime ideals over skew Ore polynomials
Communications in AlgebraIn this paper, we investigate the attached prime ideals of inverse polynomial modules over skew Ore polynomials.
Armando Reyes
exaly +3 more sources
Elimination Algorithms for Skew Polynomials with Applications in Cybersecurity
MathematicsIt is evident that skew polynomials offer promising directions for developing cryptographic schemes. This paper focuses on exploring skew polynomials and studying their properties with the aim of exploring their potential applications in fields such as ...
Raqeeb Rasheed +2 more
exaly +3 more sources
Nonassociative Algebras, Rings and Modules over Them
Mathematics, 2023 The review is devoted to nonassociative algebras, rings and modules over them. The main actual and recent trends in this area are described. Works are reviewed on radicals in nonassociative rings, nonassociative algebras related with skew polynomials ...
Sergey Victor Ludkowski
doaj +1 more source
Invariant polynomials of Ore extensions by $q$-skew derivations [PDF]
Proceedings of the American Mathematical Society, 2012 Let \(R\) be a prime ring with a symmetric Martindale quotient ring \(Q\) and \(Q[t;\sigma,\delta]\) the Ore extension of \(Q\) by a \(\sigma\)-derivation \(\delta\). \(f(t)\in Q[t;\sigma,\delta]\) is a cv-polynomial if it is associated to an automorphism \(\tau\) of \(Q\) such that \(f(t)r-\tau(r)f(t)\in Q\) for any \(r\in R\). A cv-polynomial \(f(t)\)
Chuang, Chen-Lian +2 more
openaire +1 more source
ON q-SKEW ITERATED ORE EXTENSIONS SATISFYING A POLYNOMIAL IDENTITY [PDF]
Journal of Algebra and Its Applications, 2011 For iterated Ore extensions satisfying a polynomial identity (PI) we present an elementary way of erasing derivations. As a consequence we recover some results obtained by Haynal. [PI degree parity in q-skew polynominal rings, J. Algebra319 (2008) 4199–4221].
Leroy, André, Matczuk, Jerzy
openaire +3 more sources
Ore and Goldie theorems for skew PBW extensions [PDF]
, 2013 Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW (Poincar\'e-Birkhoff-Witt) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials,
Acosta, Juan Pablo +4 more
core +1 more source
Some homological properties of skew PBW extensions [PDF]
, 2013 We prove that if R is a left Noetherian and left regular ring then the same is true for any bijective skew PBW extension A of R. From this we get Serre's Theorem for such extensions.
Armando Reyes +2 more
core +1 more source
Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups [PDF]
, 1993 We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain
A. Joseph +20 more
core +2 more sources
Semifields from skew polynomial rings [PDF]
, 2012 Skew polynomial rings were used to construct finite semifields by Petit in 1966, following from a construction of Ore and Jacobson of associative division algebras.
Lavrauw, Michel, Sheekey, John
core +4 more sources
Separably closed fields and contractive Ore modules [PDF]
, 2014 We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented ...
Bélair, Luc, Point, Françoise
core +2 more sources