Ideals and Congruence Relations
There is a bijective correspondence between ideals and congruence relations (equivalence relations that respect the ring structure) on the ring:
Given an ideal I of a ring R, let x ~ y if x − y ∈ I. Then ~ is a congruence relation on R.
Conversely, given a congruence relation ~ on R, let I = {x : x ~ 0}. Then I is an ideal of R.
Read more about this topic: Ideal (ring Theory)
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