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Modern applications of lattice theory
This thesis explores two of the modern applications of lattice theory. The first is the area of convex partitions of a lattice. We show some of the order theoretic properties of the lattice of convex partitions and then define the join in the class of extendable partitions. We completely characterize which finite modular lattices are lattices of convex partitions. Finally, if we have a finite, atomic and coatomic lattice L, we show that L can be determined, up to duality, from its convex partitions. The second part of this thesis concerns effect algebras. We show some of the order theoretic properties of effect algebras. We determine which finite modular lattices can be organized into effect algebras, as well as which finite lattices of height three can be so organized. ^
Sykes, Scott R, "Modern applications of lattice theory" (1996). Doctoral Dissertations Available from Proquest. AAI9639035.