Dimension of an algebraic set
= Dimension of an algebraic set
{title2=$\dim X$}
= Algebraic dimension
{synonym}
The supremum of the lengths of strict chains of nonempty <irreducible closed subsets>. It is the maximum of the dimensions of the <irreducible components>. For an <affine algebraic set> it equals the <Krull dimension> of its <coordinate ring>; for a <quasi-projective algebraic set> it is the supremum of these dimensions over <affine open subsets>.