R' = integralClosure(R, A)
This function packages the output integral closure in the desired way. For more details about integral closure, see integralClosure(Ring).
In the following example, there are three possible coefficient rings for $R$: $R$, $A$ and ${\mathbb Q}$.
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Note that the second and third calls to integralClosure changes the output of icMap but the fractions are the same.
All the caveats of integralClosure(Ring) are in effect and the output of icMap changes upon each call to this function.