Date on Master's Thesis/Doctoral Dissertation

8-2015

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Riedel, Thomas

Committee Member

Powers, Robert

Committee Member

Seif, Steven

Committee Member

Biro, Csaba

Committee Member

Usher, John

Subject

Automorphisms; Modular lattices

Abstract

The residuated maps from a lattice L to itself form their own lattice, which we denote Res(L). In this dissertation, we explore the order automorphisms on the lattice Res(L) where L is a finite nondistributive lattice. It is known that left and right composition of f ∈ Res(L) with automorphisms of L yields an order automorphism of Res(L). It begs the question, then, if all order automorphisms of Res(L) can be classified as such.

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