Ring theory square bracket notation

Question

What does the notation $[\mathfrak{p}]$ mean, if $\mathfrak{p}$ is a prime ideal of some (polynomial) ring $A$ (parentheses because I'm not sure if $A$ being a polynomial ring is important) ?

Answer 1

Vakil is using the notation $[\mathfrak{p}]$ to indicate the point in $\operatorname{Spec}(A)$ corresponding to the prime ideal $\mathfrak{p}\subseteq A.$ He wants to distinguish between the prime $\mathfrak{p}$ as an ideal of the ring and as a point of the topological space $\operatorname{Spec}(A).$