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arXiv · 2004.08840

The lattice of monomial clones on finite fields

Sebastian Kreinecker
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Abstract

We investigate the lattice of clones that are generated by a set of functions that are induced on a finite field $\mathbb{F}$ by monomials. We study the atoms and coatoms of this lattice and investigate whether this lattice contains infinite ascending chains, or infinite descending chains, or infinite antichains. We give a connection between the lattice of these clones and semi-affine algebras. Furthermore, we show that the sublattice of idempotent clones of this lattice is finite and every idempotent monomial clone is principal.

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Sebastian Kreinecker. 2020-04-19. The lattice of monomial clones on finite fields. https://doi.org/10.1007/s00012-021-00733-6

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