Large filters of quasiorder lattices can be generated by few elements

Gábor Czédli

Large filters of quasiorder lattices can be generated by few elements

Rings and Algebras 2024-02-26 v4

Authors: Gábor Czédli

Abstract

For a poset $(P;\leq)$ , the quasiorders (AKA preorders) extending the poset order " $\leq$ " form a complete lattice $F$ , which is a filter in the lattice of all quasiorders of the set $P$ . We prove that if the poset order " $\leq$ " is small, then $F$ can be generated by few elements.

Keywords

poset quasiorder preorder complete lattice filter generating set

Cite

@article{arxiv.2302.13911,
  title  = {Large filters of quasiorder lattices can be generated by few elements},
  author = {Gábor Czédli},
  journal= {arXiv preprint arXiv:2302.13911},
  year   = {2024}
}

Comments

18 pages, 2 figures. An error has been corrected and the theorem is stated in a new form. Furthermore, arXiv:2303.10790 made the cryptographic section superfluous, so this section has been omitted

Large filters of quasiorder lattices can be generated by few elements

Abstract

Keywords

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