A total ring of fractions of a nonzero commutative ring 
with multiplicative identity is the localization 
, where 
is the set of all nonzero elements that are not zero divisors.
It is also called a total quotient ring (Stacks Project, Tag 00CM).
The natural ring homomorphism 
is injective. Indeed,
requires 
for some 
,
which forces 
by the choice of 
.
This distinguishes the total ring of fractions from a general ring
of fractions obtained by localization at an
arbitrary multiplicatively closed set.
For an integral domain, 
and 
is its field of fractions.
For 
,
instead, the permitted denominators are the ring units
1 and 5, so 
is isomorphic to 
, despite the presence of zero
divisors.
