All Outputs (25)

The automorphisms of differential extensions of characteristic p (2024)
Journal Article

Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension K of exponent one of a field F , F of characteristic p, or of a central division algebra over a purely i... Read More about The automorphisms of differential extensions of characteristic p.

A generalization of the first Tits construction (2024)
Journal Article

Let F be a field of characteristic, not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar em... Read More about A generalization of the first Tits construction.

Albert’s twisted field construction using division algebras with a multiplicative norm (2024)
Journal Article

We generalize Albert’s twisted field construction, applying it to unital division algebras with a multiplicative norm. We give conditions for the resulting algebras to be division algebras. Four- and eight-dimensional real unital and non-unital divis... Read More about Albert’s twisted field construction using division algebras with a multiplicative norm.

Division algebras and MRD codes from skew polynomials (2023)
Journal Article

Let be a division algebra, finite-dimensional over its center, and a skew polynomial ring. Using skew polynomials, we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra... Read More about Division algebras and MRD codes from skew polynomials.

Irreducible skew polynomials over domains (2021)
Journal Article

Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ-derivation. We give criteria for skew polynomials f ∈ R of degree less or equal to four to be irreducible. We apply them to low degr... Read More about Irreducible skew polynomials over domains.

The norm of a skew polynomial (2021)
Journal Article

Let D be a finite-dimensional division algebra over its center and R=D[t;σ,δ] a skew polynomial ring. Under certain assumptions on δ and σ, the ring of central quotients D(t;σ,δ)={f/g|f∈D[t;σ,δ],g∈C(D[t;σ,δ])} of D[t;σ,δ] is a central simple algebra... Read More about The norm of a skew polynomial.

A generalisation of Amitsur's A-polynomials (2021)
Journal Article

We find examples of polynomials f in D[t;\sigma,\delta] whose eigenring is a central simple algebra over the field F = C \cap Fix(\sigma) \cap Const(\delta).

The automorphisms of generalized cyclic Azumaya algebras (2020)
Journal Article

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an Azumaya algebra of constant rank with center $C$ and $\sigma$ an automorphism of $D$, such that $\sigma|_{C}$ has fini... Read More about The automorphisms of generalized cyclic Azumaya algebras.

How a nonassociative algebra reflects the properties of a skew polynomial (2019)
Journal Article

Let D be a unital associative division ring and D[t, σ, δ] be a skew polynomial ring, where σ is an endomorphism of D and δ a left σ-derivation. For each f D[t, σ, δ] of degree m > 1 with a unit as leading coefficient, there exists a unital nonassoci... Read More about How a nonassociative algebra reflects the properties of a skew polynomial.

Diagonal Forms of Higher Degree Over Function Fields of p-adic Curves (2019)
Journal Article

We investigate diagonal forms of degree d over the function field F of a smooth projective p-adic curve: if a form is isotropic over the completion of F with respect to each discrete valuation of F , then it is isotropic over certain fields F_U , F_P... Read More about Diagonal Forms of Higher Degree Over Function Fields of p-adic Curves.

Solvable crossed product algebras revisited (2019)
Journal Article

For any central simple algebra over a field F which contains a maximal subfield M with non-trivial automorphism group G = AutF (M), G is solvable if and only if the algebra contains a finite chain of subalgebras which are generalized cyclic algebras... Read More about Solvable crossed product algebras revisited.

The multiplicative loops of Jha-Johnson semifields (2019)
Journal Article

The multiplicative loops of Jha-Johnson semifields are non-automorphic finite loops whose left and right nuclei are the multiplicative groups of a field extension of their centers. They yield examples of finite loops with non-trivial automorphism gro... Read More about The multiplicative loops of Jha-Johnson semifields.

Quotients of orders in algebras obtained from skew polynomials with applications to coding theory (2018)
Journal Article

We describe families of nonassociative finite unital rings that occur as quotients of natural nonassociative orders in generalized nonassociative cyclic division algebras over number fields. These natural orders have already been used to systematical... Read More about Quotients of orders in algebras obtained from skew polynomials with applications to coding theory.

Nonassociative cyclic extensions of fields and central simple algebras (2018)
Journal Article

We define nonassociative cyclic extensions of degree m of both fields andcentral simple algebras over fields. If a suitable field contains a primitive mth (resp., qth) root of unity, we show that suitable nonassociative generalized cyclic division al... Read More about Nonassociative cyclic extensions of fields and central simple algebras.

Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings (2018)
Journal Article

We study the automorphisms of Jha-Johnson semifields obtained from a right invariant irreducible twisted polynomial f Є K[t;σ], where K = Fqn is a finite field and σ an automorphism of K of order n, with a particular emphasis on inner automorphisms a... Read More about Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings.

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.