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Difference between revisions of "Principal translation"

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''Elementary translation''
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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 $A$.
  
====Comments====
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The terminology "elementary translation" is also used: as are "algebraic function" (of one variable) or "polynomial".
The term  "principal translation" is not used in the Western literature. A function as above would normally be called an algebraic function (of one variable) or a polynomial.
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====References====
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* 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
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article