Outputs (27)

A classification of the division algebras that are isotopic to a cyclic Galois field extension (2025)
Journal Article
Pumpluen, S. (in press). A classification of the division algebras that are isotopic to a cyclic Galois field extension. Israel Journal of Mathematics,

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree n>2 up to isomorphisms.
We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The classification is... Read More about A classification of the division algebras that are isotopic to a cyclic Galois field extension.

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.

A generalisation of Amitsur's A-polynomials (2021)
Presentation / Conference Contribution
Pumplün, S., & Owen, A. (2020, February). 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 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.