The minimal components of the Mayr-Meyer ideals. (Q1403895)

Let \(I\) be an ideal in an \(n\)-dimensional polynomial ring, generated by \(f_1,\dots, f_k\). It is well known that if the maximum degree of a generator is \(d\), then it is possible to write any \(f\) in \(I\) as \(f=\sum r_if_i\) with each \(r_i\) of degree at most deg\(f+(kd)^{(2^n)}\). Mayr and Meyer found families of ideals for which such a bound is indeed achieved. In the paper under review the minimal components and the minimal prime ideals of the Mayr-Meyer ideals are studied. In particular it is proved that the intersection of the minimal components of the Mayr-Meyer ideals does not satisfy the double exponential property, so that the doubly exponential behaviour must be due to the embedded prime ideals.