Nonassociative differential extensions of characteristic p
Let F be a field of characteristic p. We define and investigate
nonassociative differential extensions of F and of a central simple division
algebra over F and give a criterion for these algebras to be division. As
special cases, we obtain classical results for associative algebras by Amitsur
and Jacobson. We construct families of nonassociative division algebras which
can be viewed as generalizations of associative cyclic extensions of a purely
inseparable field extension of exponent one or a central division algebra.
Division algebras which are nonassociative cyclic extensions of a purely in
separable field extension of exponent one are particularly easy to obtain.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >