Abstract by Ryan Janai Kurth-Oliveira
Ryan Janai Kurth-Oliveira
Representing Pine-cone and Christmas Tree Lattices as Algebraic Structures
For an algebraic structure A, one can easily build a lattice from its subalgebras with the partial order of set inclusion. There is a constructive proof that every algebraic lattice is isomorphic to a subalgebra lattice. Although this construction works well for the purposes of the proof, in practice it will result in a surplus of functions. Given certain types of lattices, including the pinecone and the christmas tree, we will construct algebras that contain a more reasonable number of operations.