Different approaches to construct linear codes using skew polynomials can be unified by using the nonassociative algebras built from skew-polynomial rings by Petit.

Our purpose in this paper is to characterize skew PBW extensions over several weak symmetric rings. As a consequence of our treatment, we extend results the literature concerning property symmetry for commutative rings and polynomial

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an algebra constant rank with center $C$ and $\sigma$ automorphism $D$, such that $\sigma|_{C}$ has finite order. The automorphisms these are canonically induced by ring the $D[t;\sigma]$ used in their construction. achieve description inner automorphisms. Results on ...