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About: Congruence ideal     Goto   Sponge   NotDistinct   Permalink

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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.