Algebraic set
= Algebraic set
{title2=$V(I)$}
An algebraic set is a zero locus of polynomial equations, allowing reducible sets. An <affine algebraic set> uses ordinary polynomial equations; a projective algebraic set uses homogeneous equations in projective coordinates. On affine or projective space, closed sets in the <Zariski topology> are algebraic sets, and an irreducible algebraic set is an <algebraic variety> in the classical convention.