Prime ideals of Moh and the characteristic of the field

In this paper, 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.