Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

In this paper we consider skew bisubmodular functions as recently introduced by the authors and Powell. We construct a convex extension of a skew bisubmodular function which we call Lovász extension in correspondence to the submodular case. We use this extension to show that skew bisubmodular functions given by an oracle can be minimised in polynomial time.

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...

We show that error and erasure decoding of `-Interleaved Gabidulin codes, as well as list-` decoding of Mahdavifar–Vardy codes can be solved by row reducing skew polynomial matrices. Inspired by row reduction of F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into certain normal forms. We apply this to solve generalised shift registe...

In this paper, we study the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras.