The Chinese monoid of rank is generated by subject to the relations
The monoid is infinite and has polynomial growth.
In the paper under review the authors study the structure of the monoid algebra of over a field . The authors show that has only finitely many prime ideals and completely describe them using certain homogeneous congruences on . Further, it is shown that the prime radical of coincides with the Jacobson radical. As a consequence the authors derive a new representation of as a submonoid of the product for some , where denotes the bicyclic monoid, and show that satisfies a nontrivial identity.