= Total ring of fractions
{wiki=Total_ring_of_fractions}
In abstract algebra, the total ring of fractions is a construction that generalizes the concept of localization from integral domains to more general rings. Specifically, it provides a way to create a new ring that contains the original ring and allows for division by certain elements, including non-zero divisors. \#\#\# Definition: Given a ring \\( R \\) (not necessarily an integral domain) and a set \\( S \\) of elements in \\( R \\) that contains the non-zero divisors (i.e.
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