Situation 15.6.1. In the following we will consider ring maps

$\xymatrix{ B \ar[r] & A & A' \ar[l] }$

where we assume $A' \to A$ is surjective with kernel $I$. In this situation we set $B' = B \times _ A A'$ to obtain a cartesian square

$\xymatrix{ A & A' \ar[l] \\ B \ar[u] & B' \ar[l] \ar[u] }$

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