When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ideal is always prime. For example, consider f:Z->Z[sqrt(2)]. Then the contraction of 〈sqrt(2)〉 is the ideal of even integers.

algebraic number theory | ideal | ideal extension | prime ideal | ring