Principal translation

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