Algebraic set

Summary

An algebraic set is the set of common zeros, in the affine space $k^n$ over a field $k$, of a family of polynomials. The polynomials are in $n$ variables. Algebraic sets are the basic geometric objects of classical algebraic geometry. They are the closed sets of the Zariski topology on $k^n$. Over an algebraically closed field they correspond to radical ideals of the polynomial ring.