Definition 33.40.4. Let $A$ and $A_ i$, $1 \leq i \leq n$ be local rings. We say $A$ is a wedge of $A_1, \ldots , A_ n$ if there exist isomorphisms

$\kappa _{A_1} \to \kappa _{A_2} \to \ldots \to \kappa _{A_ n}$

and $A$ is isomorphic to the ring consisting of $n$-tuples $(a_1, \ldots , a_ n) \in A_1 \times \ldots \times A_ n$ which map to the same element of $\kappa _{A_ n}$.

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