Following on from the example, in algebraic geometry one studies "algebraic sets", i.e. subsets of "K""n" (where "K" is an algebraically closed field) that are defined as the common zeros of a set of polynomials in "n" variables. If "A" is such an algebraic set, one considers the commutative ring "R" of all polynomial functions "A" → "K". The "maximal ideals" of "R" correspond to the points of "A" (because "K" is algebraically closed), and the "prime ideals" of "R" correspond to the "subvarieties" of "A" (an algebraic set is called irreducible or a variety if it cannot be written as the union of two proper algebraic subsets).