  In this note we consider algebraic exponential sums over the values of
homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1,
\cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an
estimate of this exponential sum and a corresponding stratification of the
space $\mathbb{A}_{\mathbb{F}_p}^n$, which in particular illustrates a general
stratification theorem of Fouvry and Katz.
