Abstract by Madeline May
Algebraic Representations for a Finite Lattice
For any group the subgroups form a lattice under set inclusion. Further, the subalgebras of any algebra form a lattice. For a finite lattice L, Birkhoff-Frink provided a method to construct an algebra whose subalgebra is isomorphic to L. However, this method gives an excess of operations. We consider methods for certain types of lattices that provide necessary functions. In this presentation we look at power sets lattices and the Mn lattice. We also consider what happens when adding a greatest or least element to a preexisting lattice.