algebraic map (original) (raw)

A map f:X→Y between quasi-affine varieties X⊂kn,Y⊂km over a field k is called if there is a map f′:kn→km whose component functions are polynomials, such that f′ restricts to f on X.

Alternatively, f is algebraic if the pullback map f*:C⁢(Y)→C⁢(X) maps the coordinate ring of Y, k⁢[Y], to the coordinate ring of X, k⁢[X].