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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.
References

Lenstra, H. W. (1995), "Complete intersections and Gorenstein rings", in Coates, John, Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), Ser. Number Theory, I, Int. Press, Cambridge, MA, pp. 99–109, ISBN 1-57146-026-8, MR 1363497, Zbl 0860.13012

Mathematics Encyclopedia

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