Editing Congruence relation (section)

{{Short description|Equivalence relation in algebra}}
{{For|the term as used in elementary geometry|congruence (geometry)}}
{{no footnotes|date=February 2015}}

In [[abstract algebra]], a '''congruence relation''' (or simply '''congruence''') is an [[equivalence relation]] on an [[algebraic structure]] (such as a [[group (mathematics)|group]], [[ring (mathematics)|ring]], or [[vector space]]) that is compatible with the structure in the sense that [[algebraic operation]]s done with equivalent elements will yield equivalent elements.{{sfnp|ps=|Hungerford|1974|p=27}}  Every congruence relation has a corresponding [[Equivalence class|quotient]] structure, whose elements are the [[equivalence class]]es (or '''congruence classes''') for the relation.{{sfnp|ps=|Hungerford|1974|p=26}}