Let a⊆C[x1,…,xm]\mathfrak a\subseteq \mathbb C[x_1,\ldots,x_m]a⊆C[x1,…,xm] and b⊆C[y1,…,yn]\mathfrak b\subseteq \mathbb C[y_1,\ldots,y_n]b⊆C[y1,…,yn] be nonzero ideals, and regard them as ideals in…