All Outputs (6)

Algebras whose right nucleus is a central simple algebra (2017)
Journal Article

We generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of ch... Read More about Algebras whose right nucleus is a central simple algebra.

How to obtain lattices from (f,?,?)-codes via a generalization of Construction A (2017)
Journal Article

We show how cyclic (f,?,?)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain... Read More about How to obtain lattices from (f,?,?)-codes via a generalization of Construction A.

How to obtain lattices from ( f, σ, δ)-codes via a generalization of Construction A (2017)
Journal Article

We show how cyclic ( f, σ, δ)-codes over finite rings canonically induce a Z lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f . This construction generalizes the one using cert... Read More about How to obtain lattices from ( f, σ, δ)-codes via a generalization of Construction A.

Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes (2017)
Journal Article

Let S be a unital ring, S[t; σ, δ] a skew polynomial ring where σ is an injective endomorphism and δ a left σ -derivation, and suppose f ε S[t; σ, δ] has degree m and an invertible leading coefficient. Using right division by f to define the multipl... Read More about Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes.

The automorphisms of Petit's algebras (2017)
Journal Article

Let ? be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; ?]=fK[t; ?] obtained when the twisted polynomialf 2 K... Read More about The automorphisms of Petit's algebras.

Nonassociative differential extensions of characteristic p (2017)
Journal Article

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtai... Read More about Nonassociative differential extensions of characteristic p.