Relation With Homomorphisms
If ƒ: A → B is a homomorphism between two algebraic structures (such as homomorphism of groups, or a linear map between vector spaces), then the relation ≡ defined by
- a1 ≡ a2 if and only if ƒ(a1) = ƒ(a2)
is a congruence relation. By the first isomorphism theorem, the image of A under ƒ is a substructure of B isomorphic to the quotient of A by this congruence.
Read more about this topic: Congruence Relation
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