  We study pluricomplex Green functions on algebraic sets. Let $f$ be a proper
holomorphic mapping between two algebraic sets. Given a compact set $K$ in the
range of $f$, we show how to estimate the pluricomplex Green functions of $K$
and of $f^{-1}(K)$ in terms of each other, the {\L}ojasiewicz exponent of $f$
and the growth exponent of $f$. This result leads to explicit examples of
pluricomplex Green functions on algebraic sets. We also present an enhanced
version of the Bernstein-Walsh polynomial inequality specific to algebraic
sets. This article provides a theoretical framework for future investigations
of the rate of polynomial approximation of holomorphic functions on algebraic
sets in the style of Bernstein-Walsh-Siciak theorem.
