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Let      n i , 1 ≤  i ≤  r , r ≥  3 {n_i},1 \leq i \leq r,r \geq 3      , be natural numbers such that      ( n 1 , ⋯  , n r ) = 1 ({n_1}, \cdots ,{n_r}) = 1       and      n i = Σ  j = 1 r z j n j , z j {n_i} = \Sigma _{j = 1}^r{z_j}{n_j},{z_j}      . nonnegative integers, implies      z j = 0 , j ≠  i {z_j} = 0,j \ne i      , and      z i = 1 {z_i} = 1      . It is shown that for prime ideals with generic zero      x i = t n i {x_i} = {t^{{n_i}}}       and      r ≥  4 r \geq 4      , arbitrary large finite minimal sets of generators exist.

On prime ideals with generic zero 𝑥ᵢ=𝑡^{𝑛ᵢ}