The natural projection, also called the homomorphism, is a logical way of mapping an algebraic structure onto its quotient structures. The natural projection 
is defined formally for groups and rings
as follows.
For a group 
, let 
(i.e., 
be a normal subgroup of
).
Then 
is defined by 
.
Note 
(Dummit and Foote 1998, p. 84).
For a ring, let 
be an ideal of a ring 
. 
is defined be 
. Note 
(Dummit and Foote 1998, p. 244).
