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).