  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.
