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Comment by aleph_minus_one

> Is there’s something more to that?

Yes: this is about building the quotient field (field of fractions) [1] for some integral domain, or more generally, building the localization ([2], [3]) of a commutative ring with respect to some given set that is closed under multiplication (the special case of the quotient field for a ring R is obtained when one chooses R\{0} as such a set).

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[1] https://en.wikipedia.org/w/index.php?title=Field_of_fraction...

[2] https://en.wikipedia.org/w/index.php?title=Field_of_fraction...

[3] https://en.wikipedia.org/w/index.php?title=Localization_(com...

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