  The differential Brauer monoid of a differential commutative ring R s
defined. Its elements are the isomorphism classes of differential Azumaya R
algebras with operation from tensor product subject to the relation that two
such algebras are equivalent if matrix algebras over them are differentially
isomorphic. The Bauer monoid, which is a group, is the same thing without the
differential requirement. The differential Brauer monoid is then determined
from the Brauer monoids of R and its ring of constants and the submonoid whose
underlying Azumaya algebras are matrix rings.
