Finitely Related Clones and Algebras with Cube Terms

@article{Markovic2012FinitelyRC,
title={Finitely Related Clones and Algebras with Cube Terms},
author={Petar Markovic and Mikl{\'o}s Mar{\'o}ti and Ralph McKenzie},
journal={Order},
year={2012},
volume={29},
pages={345-359}
}

Aichinger et al. (2011) have proved that every finite algebra with a cubeterm (equivalently, with a parallelogram-term; equivalently, having few subpowers) is finitely related. Thus finite algebras with cube terms are inherently finitely related—every expansion of the algebra by adding more operations is finitely related. In this paper, we show that conversely, if A is a finite idempotent algebra and every idempotent expansion of A is finitely related, then A has a cube-term. We present further… CONTINUE READING