  Mayr and Meyer found ideals with the doubly exponential ideal membership
property. In the analysis of the associated primes of these ideals (in
math.AC/0209344), a new family of ideals arose. This new family is presented
and analyzed in this paper. It is proved that this new family also satisfies
the doubly exponential ideal membership property. Furthermore, the set of
associated primes of this family can be computed inductively.
