2018/11/30 by Martha L. H. Kilpack, Kilpack, Martha L. H., Ryan Kurth-Oliveira +3
Computer Science · #06B99 #08A30 #Advanced Algebra and Logic #FOS: Mathematics #General Mathematics (math.GM) #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1812.00803
openalex publication_date 2018/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an arbitrary group, the subgroups form a lattice with order determined by set inclusion. Not every lattice is isomorphic to the subgroup lattice for a group. However, Birkhoff and Frink proved that any compactly generated lattice is isomorphic to a subalgebra lattice for some algebraic structure. An algebraic structure is a set A with operations from An to A where nis a non-negative integer. Although the proof by Birkhoff and Frink is constructive, many of the operations described are not needed for an algebraic structure to represent a given lattice. In this paper we utilize concepts in the proof by Birkhoff and Frink to describe and count functions that are used to create algebraic structure representations for certain finite lattice types.