Full ideals of polynomial rings

An ideal I of the ring K[x_l, . . . ,x_n]of polynomials over a field K in n indeterminates is a full ideal if I is closed under substitution, f ∈ I, g_l, . . . ,g_n) ∈ K[x_l, . . . ,x_n] imply f(g_l, . . . ,g_n ∈ I. In this paper we continue the investigation of full ideals of K[x_l, . . . ,x_n]. In particular we determine several classes of full ideals of K[x, y] (K a finite field) and investigate properties of these classes.