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Congruence relation
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (February 2015) |
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]
- ^ Hungerford (1974), p. 27
- ^ Hungerford (1974), p. 26
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