The Stacks project

Definition 53.19.10. Let $k$ be a field. Let $X$ be a $1$-dimensional algebraic $k$-scheme. Let $x \in X$ be a closed point. We say $x$ is a split node if $x$ is a node, $\kappa (x) = k$, and the equivalent assertions of Remark 53.19.9 hold for $A = \mathcal{O}_{X, x}$.