TITLE: Normalization of a Ring
QUESTION [6 upvotes]: 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! :)

REPLY [3 votes]: 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.