When 
is a ring homomorphism and 
is an ideal in 
, then 
is an ideal in 
, called the contraction of 
and sometimes denoted 
.
The contraction of a prime ideal is always prime. For example, consider ![f:Z->Z[sqrt(2)]](/images/equations/IdealContraction/Inline8.svg)
.
Then the contraction of 
is the ideal of even integers.
