The process of order, reverse and subtract is taken from integers right to polynomial rings with coefficients in a finite field. We do such essentially for prime fields but we also comment a little on non prime fields. Given that Kaprekar’s routine depends so much in the order of the set we work in, we first give an order to the polynomial rings in question and then, we focus on the number and length of the cycles associated to this routine, specifically for the two and three digits polynomials case.
