Namespaces
Variants
Actions

Translation

From Encyclopedia of Mathematics
Revision as of 16:58, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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, cf. Principal translation). 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)
[2] A.I. Mal'tsev, "Algebraic systems" , Springer (1973) (Translated from Russian)
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