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Outputs (23)

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.

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.