The lattice of monomial clones on finite fields
Rings and Algebras
2021-09-03 v2
Abstract
We investigate the lattice of clones that are generated by a set of functions that are induced on a finite field 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.
Keywords
Cite
@article{arxiv.2004.08840,
title = {The lattice of monomial clones on finite fields},
author = {Sebastian Kreinecker},
journal= {arXiv preprint arXiv:2004.08840},
year = {2021}
}
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32 pages