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What is the exact definition of a normalization of a Ring? I have to show this:

normalization of multiplicative subset of domain

And the answer already helped, but I don't know what $S^{-1}R'$ is exactly, because I didn't find a good definition for $R'$...

Thanks for any help! :)

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I believe that you really should read the definitions and be sure of what you're trying to prove before trying to prove it. Anyhow, the definition of normalization: If A is an integral domain, we say that A is normal if it is integrally closed in its field of fractions. For a domain A , the normalization of A, $\tilde{A}$ is the integral closure of A in its field of fractions.

In QiL's answer there, he gives you a straightforward way to do it. R' is the integral closure of R in its field of fractions.