Congruence ideal

In algebra, the congruence ideal of a surjective ring homomorphism "f" : "B" → "C" of commutative rings is the image under "f" of the annihilator of the kernel of "f".
It is called a congruence ideal because when "B" is a Hecke algebra and "f" is a homomorphism corresponding to a modular form, the congruence ideal describes congruences between the modular form of "f" and other modular forms.