Difference between revisions of "Principal translation"
From Encyclopedia of Mathematics
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A mapping $\phi$ of an [[algebraic system]] $\mathbf{A} = (A,\Omega)$ into itself, of the form | A mapping $\phi$ of an [[algebraic system]] $\mathbf{A} = (A,\Omega)$ into itself, of the form | ||
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where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$. | where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$. | ||
| − | + | The terminology "elementary translation" is also used: as are "algebraic function" (of one variable) or "polynomial". | |
| − | The | + | |
| + | ====References==== | ||
| + | * Cohn, Paul M. Universal algebra. Rev. ed. D. Reidel (1981) {{ISBN|90-277-1213-1}} {{ZBL|0461.08001}} | ||
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Latest revision as of 16:59, 23 November 2023
Elementary translation
A mapping $\phi$ of an algebraic system $\mathbf{A} = (A,\Omega)$ into itself, of the form $$ \phi : x \mapsto F(a_1,\ldots,a_{k-1},x,a_{k+1},\ldots,a_n) $$ where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$.
The terminology "elementary translation" is also used: as are "algebraic function" (of one variable) or "polynomial".
References
- Cohn, Paul M. Universal algebra. Rev. ed. D. Reidel (1981) ISBN 90-277-1213-1 Zbl 0461.08001
How to Cite This Entry:
Principal translation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_translation&oldid=41769
Principal translation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_translation&oldid=41769
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article