Nonassociative cyclic algebras and the semiassociative Brauer monoid

We look at classes of semiassociative algebras, with an emphasis on those that are canonical generalizations of associative (generalized) cyclic algebras. We investigate their behaviour in the semiassociative Brauer monoid defined by Blachar, Haile, Matri, Rein, and Vishne. A possible generalization of this monoid in characteristic p that includes nonassociative differential algebras is briefly considered.

SemiassociativeAlgebras.pdf