Situation 33.37.1. Here we are given a commutative diagram of rings

\[ \xymatrix{ A \ar[r] & K \\ R \ar[u] \ar[r] & B \ar[u] } \]

where $K$ is a field and $A$, $B$ are subrings of $K$ with fraction field $K$. Finally, $R = A \times _ K B = A \cap B$.

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