We propose a variation of Construction A of lattices from linear codes defined using the quotient Λ/pΛ of some order Λ inside a cyclic division F -algebra, for p a prime ideal of a number field F . To obtain codes over this quotient, we first give an isomorphism between Λ/pΛ and a ring of skew polynomials. We then discuss definitions and basic properties of skew polynomial codes, which are need...

We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection algebras, and universal enveloping algebras of Lie algebras with group actions. We giv...

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

The RHIC coupling correction system has been commissioned during the Year 2000 run, which marked the successful first year of operation of the machine. The RHIC coupling correction system is described with particular emphasis on its flexibility, which allows using both global and local coupling compensation techniques. Coupling measurements and correction data are presented for the RHIC Blue an...

The empirical distribution of daily returns from financial market variables such as exchange rates, equity prices, and interest rates, is often skewed, having one heavy, and one semiheavy, or more Gaussian-like tail. The NIG distribution, that has two semi-heavy tails, models skewness rather well, but only in cases where the tails are not too heavy. On the other hand, the skew Student’s t-distr...

Building on recent work of Jaikin-Zapirain, we provide a homological criterion for ring to be pseudo-Sylvester domain, that is, admit division fractions over which all stably full matrices become invertible. We use the study skew Laurent polynomial rings free ideal (firs). As an application our methods, prove crossed products with free-by-{infinite cyclic} and surface groups are domains uncondi...

Let $R$ be a prime ring, $Q_r$ its right Martindale quotient $L$ non-central Lie ideal of $R$, $n\geq 1$ fixed integer, $F$ and $G$ two generalized skew derivations with the same associated automorphism, $p\in R$ element. If $p\bigl(F(x)F(y)-G(y)x\bigr)^n=0$, for any $x,y \in L$, then there exist $a,c\in Q_r$ such that $F(x)=ax$ $G(x)=cx$, $x\in R$, $pa=pc=0$, unless when satisfies standard pol...

Given a Hilbertian field k and finite set S of Krull valuations , we show that every split embedding problem G → Gal ( L / ) over with abelian kernel has solution F such v ∈ is totally in . Two applications are then given. Firstly, solve non-constant variant the Beckmann–Black for solvable groups: given non-trivial group Galois extension shown to occur as specialization at some t 0 E T ⊈ ‾ Seco...

Fast computation of two-dimensional (2-D) generalized discrete Fourier transforms (GDFTs) and generalized discrete Hartley transforms (GDHTs) are discussed in terms of a new method which is derived based on index permutation, linear congruences, and polynomial transforms. Further, the 2-D skew circular convolution computed by the proposed skew polynomial transform is also included. ( 2000 Elsev...