6 papers
Menichetti's nonassociative -crossed product algebras and Menichetti codes
Susanne Pumpluen
We demonstrate the use of nonassociative algebras in code design and consider codes with nonassociative ambient algebras other than the well-known skew polycyclic codes. We define…
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 up to isomorphisms. We achieve a ``tight'' classification wh…
A closer look at Witt rings for forms of higher degree
Susanne Pumpluen
Witt rings for nondegenerate forms of degree over a field of characteristic 0 or greater than were defined by Harrison and Pareigis. We revisit and discuss their defin…
Nonassociative cyclic algebras and the semiassociative Brauer monoid
S Pumpluen
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 semia…
A parametrization of nonassociative cyclic algebras of prime degree
Monica Nevins, Susanne Pumpluen
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…
The automorphisms of differential extensions of characteristic
Susanne Pumpluen
Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension of exponent one of a field …