# Congruence relation

## Equivalence relation in algebra / From Wikipedia, the free encyclopedia

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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]}

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For the term as used in elementary geometry, see congruence (geometry).