Remove the characteristic-zero hypothesis in Moh’s construction of P_n

Determine whether the characteristic-zero hypothesis can be removed from Moh’s construction of prime ideals P_n ⊂ K[[x,y,z]], where P_n is defined as the kernel of the homomorphism ρ_n: K[[x,y,z]] → K[[t]] given by ρ_n(x) = t^{nm} + t^{nm+λ}, ρ_n(y) = t^{(n+1)m}, and ρ_n(z) = t^{(n+2)m} with m = (n+1)/2 and λ an integer greater than n(n+1)m satisfying gcd(λ, m) = 1; specifically, ascertain whether an analogous construction exists over fields K of positive characteristic.

Background

Moh constructed, for odd n over a field of characteristic zero, a family of prime ideals P_n in the three-variable power series ring K[[x,y,z]] as kernels of a parametrization ρ_n with explicitly specified exponents. These ideals provide examples requiring at least n generators. The authors note that Moh explicitly left open whether the characteristic-zero assumption is essential.

The paper’s broader program revisits binomial determinants and related linear algebra with the aim of facilitating generalizations of Moh’s work; nevertheless, the characteristic issue remains explicitly identified as an open question in the introduction.