I'm trying to figure out if I need to use traits of Characteristic and/or Minimal Polynomials.
Suppose that and . Prove that if , then is nilpotent, and for all
I'm not looking for a solution, I simply want a head start.
For k=0,1,2,..., let . Show that the given condition (which is equivalent to ) implies that the sequence is strictly increasing for . You should be able to do this directly, without needing to consider characteristic or minimal polynomials.