All Outputs (27)

A parametrization of nonassociative cyclic algebras of prime degree (2024)
Journal Article
Nevins, M., & Pumplün, S. (2025). A parametrization of nonassociative cyclic algebras of prime degree. Journal of Algebra, 664(Part A), 631-654. https://doi.org/10.1016/j.jalgebra.2024.10.021

We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism classes of nonassociative cyclic algebras of odd prime degree m when t... Read More about A parametrization of nonassociative cyclic algebras of prime degree.

Nonassociative cyclic algebras and the semiassociative Brauer monoid (2024)
Journal Article
Pumplün, S. (2024). Nonassociative cyclic algebras and the semiassociative Brauer monoid. Rendiconti del Circolo Matematico di Palermo, 73, 3253-3275. https://doi.org/10.1007/s12215-024-01105-4

We look at classes of semiassociative algebras, with an emphasis on those that canonically generalize associative (generalized) cyclic algebras, and at their behaviour in the semiassociative Brauer monoid defined by Blachar, Haile, Matzri, Rein, an... Read More about Nonassociative cyclic algebras and the semiassociative Brauer monoid.

The automorphisms of differential extensions of characteristic p (2024)
Journal Article
Pumplün, S. (2024). The automorphisms of differential extensions of characteristic p. Results in Mathematics, 79(5), Article 196. https://doi.org/10.1007/s00025-024-02234-z

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 in... Read More about The automorphisms of differential extensions of characteristic p.

A generalization of the first Tits construction (2024)
Journal Article
Pumpluen, S., & Moran, T. (2024). A generalization of the first Tits construction. Axioms, 13(5), Article 299. https://doi.org/10.3390/axioms13050299

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
Pumplün, S. (2024). Albert’s twisted field construction using division algebras with a multiplicative norm. Journal of Algebra and Its Applications, https://doi.org/10.1142/S0219498825502536

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
Thompson, D., & Pumplün, S. (2023). Division algebras and MRD codes from skew polynomials. Glasgow Mathematical Journal, 65(2), 480-500. https://doi.org/10.1017/S001708952300006X

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
Brown, C., & Pumpluen, S. (2021). Irreducible skew polynomials over domains. Analele Universităţii "Ovidius" Constanta - Seria Matematica, 29(3), 75–89. https://doi.org/10.2478/auom-2021-0035

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
Pumpluen, S., & Thompson, D. (2022). The norm of a skew polynomial. Algebras and Representation Theory, 25(4), 869–887. https://doi.org/10.1007/s10468-021-10051-z

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)
Presentation / Conference Contribution
Pumpluen, S., & Owen, A. A generalisation of Amitsur's A-polynomials. Presented at 3rd International Workshop on Nonassociative Algebras in Málaga, Malaga, Spain

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
Pumpluen, S. (2021). The automorphisms of generalized cyclic Azumaya algebras. Journal of Pure and Applied Algebra, 225(4), Article 106540. https://doi.org/10.1016/j.jpaa.2020.106540

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
Brown, C., & Pumpluen, S. (2021). How a nonassociative algebra reflects the properties of a skew polynomial. Glasgow Mathematical Journal, 63(1), 6-26. https://doi.org/10.1017/S0017089519000478

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
Pumplün, S., & Pumpluen, S. (2020). Diagonal Forms of Higher Degree Over Function Fields of p-adic Curves. International Journal of Number Theory, 16(1), 161-172. https://doi.org/10.1142/S1793042120500098

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
Brown, C., & Pumpluen, S. (2019). Solvable crossed product algebras revisited. Glasgow Mathematical Journal, 1-21. https://doi.org/10.1017/S0017089519000089

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
Pumpluen, S. (2019). The multiplicative loops of Jha-Johnson semifields. Communications in Contemporary Mathematics, 721, 227-242

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
Pumpluen, S. (2018). Quotients of orders in algebras obtained from skew polynomials with applications to coding theory. Communications in Algebra, 46(11), 5053-5072. https://doi.org/10.1080/00927872.2018.1461882

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
Brown, C., & Pumpluen, S. (2019). Nonassociative cyclic extensions of fields and central simple algebras. Journal of Pure and Applied Algebra, 223(6), 2401-2412. https://doi.org/10.1016/j.jpaa.2018.08.018

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
Brown, C., Pumpluen, S., & Steele, A. (2018). Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings. Communications in Algebra, 46(10), 4561-4576. https://doi.org/10.1080/00927872.2018.1448845

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
Pumpluen, S. (2018). Algebras whose right nucleus is a central simple algebra. Journal of Pure and Applied Algebra, 222(9), https://doi.org/10.1016/j.jpaa.2017.10.019

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,σ,δ)-codes via a generalization of Construction A (2017)
Journal Article
Pumpluen, S. (2018). How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A. Applicable Algebra in Engineering, Communication and Computing, 29(4), https://doi.org/10.1007/s00200-017-0344-9

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 certain... Read More about How to obtain lattices from (f,σ,δ)-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
Pumpluen, S. (2018). How to obtain lattices from ( f, σ, δ)-codes via a generalization of Construction A. Applicable Algebra in Engineering, Communication and Computing, 29, 313-333. https://doi.org/10.1007/s00200-017-0344-9

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.