arXiv subjects

Sebastian Kreinecker

Publications and source records attributed to Sebastian Kreinecker.

3 recordsLinked to original sources

arXiv2021

The lattice of monomial clones on finite fields

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.

math.RA↗

arXiv2019

Closed function sets on groups of prime order

We give a full description of all sets of functions on the group $(\mathbb{ Z}_p, +)$ of prime order which are closed under the composition with the clone generated by $+$ from both sides. Thereby, we also get a description of all iterative algebras on $\mathbb{Z}_p$ which are closed under the composition with the clone generated by $+$ from both sides. As another consequence, there are infinitely many non finitely generated clones above $\operatorname{Clo}({\mathbb{ Z}_p \times \mathbb{ Z}_p, +})$ for $p > 2$.

math.RA↗

arXiv2017

Subnearrings of $(\mathbb{Z}[x],+,\circ)$

We show that the nearring $(\mathbb{Z}[x],+,\circ)$ of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that are generated by subsets of $\{1,x,x^2,x^3\}$.

math.RA↗