Congruence relation

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation.

The prototypical example of a congruence relation is congruence modulo ${\displaystyle n}$ on the set of integers. For a given positive integer ${\displaystyle n}$, two integers ${\displaystyle a}$ and ${\displaystyle b}$ are called congruent modulo ${\displaystyle n}$, written

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