Suppose \(\eta\in X\) is a generization of \(x\in X\), i.e. that \(x\in \overline{\{\eta\}}\). Then for each open set \(U\subset X\), \(x\in U \implies \eta \in U\), giving us a map
\begin{align*} \mathcal O_X(U) \to \mathcal O_{X, \eta}. \end{align*}Taking direct limits over all open sets containing \(x\) then gives us a ring map
\begin{align*} \mathcal O_{X,x} \to \mathcal O_{X, \eta} \end{align*}called the generization map. This gives \(\mathcal O_{X, \eta}\) the structure of an \(\mathcal O_{X,x}\)-algebra.