We reprove and generalize a result of Moh which gives a lower bound on the minimal number of generators of an ideal in a power series ring in three variables Formula: see text over a field Formula: see text. As a consequence, in each characteristic of the field Formula: see text, we obtain a minimal generating set for the prime ideal Formula: see text of Moh. We deduce that the minimal number of generators of Formula: see text might decrease depending on the characteristic of Formula: see text. This contradicts a statement of Sally and leaves as an open problem to find families of prime ideals in Formula: see text with an unbounded minimal number of generators, when Formula: see text has characteristic other than zero. Finally, we show that these minimal generating sets of Formula: see text are standard basis with the negative degree reverse lexicographic order.
Gonzalez et al. (Thu,) studied this question.