Is it true that every localization of an integral domain is isomorphic to a subring of its field of fractions? How are the localizations of an integral domain related to its field of fractions? Is there a handy criterion to tell whether a subring of an integral domain has the same field of fractions as the overring? I've read that $k[x^2,x^3]\subset k[x]$ ($k$ a field, algebraically closed if this matters) have the same field of fractions, how come? I am very curious about these things.
[Math] Localization of an integral domain and fields of fractions
abstract-algebracommutative-algebraring-theory
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