The lattice of monomial clones on finite fields

Sebastian Kreinecker
2021 Algebra Universalis  
AbstractWe investigate the lattice of clones that are generated by a set of functions that are induced on a finite field $${\mathbb {F}}$$ 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.
doi:10.1007/s00012-021-00733-6 fatcat:ywqmpiv75bdu7evv4ko3v6irk4