Page "Extension and contraction of ideals" Paragraph 1

Let A and B be two commutative rings with unity, and let f: A → B be a ( unital ) ring homomorphism.

If is an ideal in A, then need not be an ideal in B ( e. g. take f to be the inclusion of the ring of integers Z into the field of rationals Q ).

The extension of in B is defined to be the ideal in B generated by.

Explicitly,