Let $A$ be a commutative ring, $I \subset A$ a finitely generated ideal. Define $\hat{A} := \varprojlim A/I^n$.
What is the best way to proof that $A/I^nA \cong \hat{A}/I^n \hat{A}$ for all $n$?
Let $A$ be a commutative ring, $I \subset A$ a finitely generated ideal. Define $\hat{A} := \varprojlim A/I^n$.
What is the best way to proof that $A/I^nA \cong \hat{A}/I^n \hat{A}$ for all $n$?
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