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.
Example
References
Congruence ideal Wikipedia(Text) CC BY-SA