Congruence relation

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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 in the sense that algebraic operations done with equivalent elements will yield equivalent elements.^[1] Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation.^[2]