Let Σ be a fixed signaturePlanetmathPlanetmathPlanetmath, and 𝔄 a structureMathworldPlanetmath for Σ. A congruencePlanetmathPlanetmathPlanetmath on 𝔄 is an equivalence relationMathworldPlanetmath such that for every natural numberMathworldPlanetmath n and n-ary function symbol F of Σ, if aiai then F𝔄(a1,an)F𝔄(a1,an).

Title congruence
Canonical name Congruence12
Date of creation 2013-03-22 13:46:38
Last modified on 2013-03-22 13:46:38
Owner almann (2526)
Last modified by almann (2526)
Numerical id 9
Author almann (2526)
Entry type Definition
Classification msc 03C05
Classification msc 03C07
Related topic CongruenceRelationOnAnAlgebraicSystem