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AAA76 - 76th Workshop on General Algebra (76. Arbeitstagung Allgemeine Algebra)
May 22-25, 2008
Department of Algebra, Johannes Kepler University Linz
Linz, Austria

Organizers
Erhard Aichinger, Peter Mayr, Matt Nickodemus, Günter Pilz

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An instance of the clone membership problem
by
Erhard Aichinger
Johannes Kepler University Linz, Austria

Let C be the clone on the integers that is generated by addition, subtraction, and squaring. We represent the unary functions in this clone by polynomials in Z[x] and write ○ for the composition of unary functions. Then we see that x8 = x2 ○(x2 ○x2) and 2 x5 = - x2 - ( x2 ○x2 ○x2 ) + ( x2 ○(x + x2 ○x2 ) ) lie in C. However, x5 does not lie in C.

We characterize the unary functions in C, and obtain a similar charactarization for the clone generated by {1, x, x3}.

Date received: May 13, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-61.