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A mapping of an algebraic system onto itself that is either the identity mapping or can be expressed as the product of a finite number of principal translations (also called elementary translations). An equivalence relation on an algebraic system is a congruence (in algebra) if and only if it is closed with respect to all translations (or with respect to merely principal translations).


[1] P.M. Cohn, "Universal algebra", Reidel (1981) ISBN 90-277-1213-1 Zbl 0461.08001
[2] A.I. Mal'tsev, "Algebraic systems", Springer (1973) (Translated from Russian) Zbl 0266.08001
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This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article