The spectrum of a ring is the set of proper prime ideals, Spec(R) = {p:p is a prime ideal in R}. The classical example is the spectrum of polynomial rings. For instance, Spec(C[x]) = {〈x - a〉:a element C} union {〈0〉}, and Spec(C[x, y]) = {〈x - a, y - b〉, (a, b) element C^2} union {〈f(x, y)〉:f is irreducible} union {〈0〉}. The points are, in classical algebraic geometry, algebraic varieties. Note that 〈x - a, y - b〉 are maximal ideals, hence also prime. The spectrum of a ring has a topology called the Zariski topology.

affine scheme | category theory | commutative algebra | conic section | ideal | prime ideal | scheme | variety | Zariski topology