# Translation

From Encyclopedia of Mathematics

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).

#### References

[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 |

**How to Cite This Entry:**

Translation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Translation&oldid=42703

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article