Definition:Prime Spectrum of Ring

Definition
Let $A$ be a commutative ring with unity.

The prime spectrum or spectrum of $A$ is the set of prime ideals of $A$:


 * $\operatorname{Spec}(A) = \{\mathfrak p \lhd A : \mathfrak p \text{ is prime}\}$

where $I \lhd A$ indicates that $I$ is an ideal of $A$.

$\operatorname{Spec}(A)$ is rarely considered as a set: it is understood to be a topological space with the Zariski topology.