S. Pumpluen

activity

20072026

most citedFinite nonassociative algebras obtained from skew polynomials and possible applications to

(f, σ, δ)

-codes

13 citations · 24 across the 14 of their papers we have counts for

collaborators

15 papers

math.RA2026

Three-Dimensional Geometry in Exceptional Algebra

John C. Baez, Susanne Pumpluen

We review some topics in "exceptional mathematics'' from the perspective of 3-dimensional geometry: the octonions $O$ , the split octonions $O^{'}$ , the bioctonions $…

math.RA2026

Explicit constructions of anti-automorphisms of cyclic and generalized cyclic algebras

Susanne Pumpluen

We present norm criteria for the existence of anti-automorphisms, as well as explicit constructions of anti-automorphisms, both on cyclic and generalized cyclic algebras. Our appro…

math.RA2025

A closer look at some cyclic semifields

Susanne Pumpluen

We prove that the choice of the automorphism $σ$ in the construction of a Petit semifield is important when counting isomorphism classes. Different choices of generators $σ$ of the…

math.RA2025

Using cyclic $(f, σ)$ -codes over finite chain rings to construct $Z_{p}$ - and $F_{q} [[t]]$ -lattices

Susanne Pumpluen

We construct $Z_{p}$ -lattices and $F_{q} [[t]]$ -lattices from cyclic $(f, σ)$ -codes over finite chain rings, employing quotients of natural nonassociative orders an…

math.RA2024

Menichetti's nonassociative $G$ -crossed product algebras and Menichetti codes

Susanne Pumpluen

We define the nonassociative Menichetti algebras which can be viewed as nonassociative crossed product algebras and then use them as ambient algebras for new linear error-correctin…

math.RA2024

A classification of the division algebras that are isotopic to a cyclic Galois field extension

Susanne Pumpluen

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 wh…

Three-Dimensional Geometry in Exceptional Algebra

Explicit constructions of anti-automorphisms of cyclic and generalized cyclic algebras

A closer look at some cyclic semifields

Using cyclic (f,σ)-codes over finite chain rings to construct Zp​- and Fq​[[t]]-lattices

Menichetti's nonassociative G-crossed product algebras and Menichetti codes

A classification of the division algebras that are isotopic to a cyclic Galois field extension

Using cyclic $(f, σ)$ -codes over finite chain rings to construct $Z_{p}$ - and $F_{q} [[t]]$ -lattices

Menichetti's nonassociative $G$ -crossed product algebras and Menichetti codes