On differential lattices

Aiping Gan, Li Guo

Research output: Contribution to journalArticlepeer-review


This paper studies the differential lattice, defined to be a lattice L equipped with a map d: L→ L that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications of differential lattices are obtained for some basic lattices. Several families of derivations on a lattice are explicitly constructed, giving realizations of the lattice as lattices of derivations. Derivations on a finite distributive lattice are shown to have a natural structure of lattice. Moreover, derivations on a complete infinitely distributive lattice form a complete lattice. For a general lattice, it is conjectured that its poset of derivations is a lattice that uniquely determines the given lattice.

Original languageEnglish (US)
Pages (from-to)7043-7058
Number of pages16
JournalSoft Computing
Issue number15
StatePublished - Aug 2022

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Software
  • Geometry and Topology


  • Congruence
  • Derivation
  • Differential algebra
  • Differential lattice
  • Lattice


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