Nonassociative cyclic algebras and the semiassociative Brauer monoid

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 semiassociative Brauer monoid defined by Blachar, Haile, Matzri, Rein, and Vishne. A possible way to generalize this monoid in characteristic $p$ that includes nonassociative differential algebras is briefly considered.