algebraic map

A map $f:X\to Y$ between quasi-affine varieties $X\subset k^n,Y\subset k^m$ over a field $k$ is called if there is a map $f^{\prime }:k^n\to k^m$ whose component functions are polynomials, such that $f^{\prime }$ restricts to $f$ on $X$.

Alternatively, $f$ is algebraic if the pullback map $f^{*}:C(Y)\to C(X)$ maps the coordinate ring of $Y$, $k[Y]$, to the coordinate ring of $X$, $k[X]$.