Topic summary
Algebraic set
Extracted from the Wikipedia article Algebraic variety.
Affine varieties
A subset V of A is called an affine algebraic set if V = Z(S) for some S. A nonempty affine algebraic set V is called irreducible if it cannot be written as the union of two proper algebraic subsets. An irreducible affine algebraic set is also called an affine variety. (Some authors use the phrase affine variety to refer to any affine algebraic set, irreducible or not.)