Namespaces
Variants
Actions

Translation

From Encyclopedia of Mathematics
Revision as of 16:59, 23 November 2023 by Chapoton (talk | contribs) (→‎References: isbn link)
(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). 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