Dugas, Manfred.Aceves, Kelly Fouts.2013-09-242013-09-242013-082013-09-24http://hdl.handle.net/2104/8807For a field F and the polynomial ring F [x] in a single indeterminate, we define Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is infinite. If F is finite, then Ḟ [x] has cardinality continuum. We study the ring Ḟ[x] for finite fields F. For the case that F is finite, we discuss many properties and the structure of Ḟ [x].en-USBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.Finite field.Polynomial ring.Endomorphism ring.Properties of a ring.Chinese remainder theorem.ThesisWorldwide access