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On the integral dependence of power series rings
We prove the following results: (1) Let R ⊂ S be two commutative rings. Suppose that dim R = 0.If f(X) ∈ S[[X]]is integral over R[[X]], then every coefficient of f(X) is integral over R. (2) Let dim R ≥ 1. There exists a ring S containing R and a …