Difference between revisions of "Translation"
From Encyclopedia of Mathematics
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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 | + | 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 translation]]s (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==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> P.M. Cohn, "Universal algebra" , Reidel (1981)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algebraic systems" , Springer (1973) (Translated from Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> P.M. Cohn, "Universal algebra", Reidel (1981) ISBN 90-277-1213-1 {{ZBL|0461.08001}}</TD></TR> | ||
| + | <TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algebraic systems", Springer (1973) (Translated from Russian) {{ZBL|0266.08001}}</TD></TR> | ||
| + | </table> | ||
| + | |||
| + | {{TEX|done}} | ||
Revision as of 19:34, 9 January 2018
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=12291
Translation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Translation&oldid=12291
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article