Corollary 1

Let $A$ be a reduced Noetherian ring, $p_i$ $(1 \leq i \leq n)$ its distinct minimal prime ideals, $K$, the field of fractions of the integral domain $A/p_i$ (canonically isomorphic to the local ring $A_{p_i}$ (Chapter IV, § 2, no. 5, Proposition 10)) and $A'_i$ the integral closure of $A$ in $K$, $(1 \leq i \leq n)$. Then the canonical isomorphism of the total ring of fractions $B$ of $A$ onto $\prod_{i=1}^n K_i$ (loc. cit.) maps the integral closure of $A$ in $B$ onto the product ring $\prod_{i=1}^n A'_i$.