The deformation theory of an algebra is controlled by the Gerstenhaber bracket, a Lie bracket on Hochschild cohomology. We develop techniques for evaluating brackets semidirect product algebras recording actions finite groups over fields positive characteristic. cohomology and these skew group can be complicated when characteristic underlying field divides order. show how to investigate using t...

We evaluate the hyperpfaffian of a skew-symmetric k-ary function polynomial f of degree k/2 · (n−1). The result is a product of the Vandermonde product and a certain expression involving the coefficients of the polynomial f . The proof utilizes a sign reversing involution on a set of weighted, oriented partitions. When restricting to the classical case when k = 2 and the polynomial is (xj − xi)...

Given an iterated skew polynomial ring C[y1; τ1, δ1] . . . [yn; τn, δn] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m+ 〈y1, y2, . . . , yn〉 is an iterated skew power series ring. When C is a field, this completion is a local, noetherian, Auslander regular domain with Krull, classical Krull and global dimension all equ...

This paper suggests a detailed algorithm for computation of the Jacobson form of the polynomial matrix associated with the transfer matrix describing the multi-input multi-output nonlinear control system, defined on homogeneous time scale. The algorithm relies on the theory of skew polynomial rings.

In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...

We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In p...

After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of their main algebraic and geometric properties. Finally, for module skew codes constructed only with an automorphism, we give some BCH type lower bounds for their...

This paper presents integral charaterizations for nonuniform dichotomy with growth rates and their correspondents the particular cases of exponential polynomial skew-evolution cocycles in Banach spaces. The connections between these three concepts are presented.

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...