The Stacks project

Exercise 111.6.24. Show that ${\mathfrak p}$ is a generalization of ${\mathfrak q}$ in $\mathop{\mathrm{Spec}}(A)$ if and only if ${\mathfrak p}\subset {\mathfrak q}$. Characterize closed points, maximal ideals, generic points and minimal prime ideals in terms of generalization and specialization. (Here we use the terminology that a point of a possibly reducible topological space $X$ is called a generic point if it is a generic points of one of the irreducible components of $X$.)