Dissertation/Thesis Abstract

On a Ring Associated to F[x]
by Fouts, Kelly Jean, Ph.D., Baylor University, 2013, 37; 3593302
Abstract (Summary)

For a field F and the polynomial ring F [x] in a single indeterminate, we define [special characters omitted] = {α ∈ EndF(F [x]) : α(f) ∈ f F [x ] for all fF [ x]}. Then [special characters omitted] is naturally isomorphic to F [x] if and only if F is infinite. If F is finite, then [special characters omitted] has cardinality continuum. We study the ring [special characters omitted] for finite fields F. For the case that F is finite, we discuss many properties and the structure of [special characters omitted].

Indexing (document details)
Advisor: Dugas, Manfred H.
Commitee: Anderson, William, Dugas, Manfred H., Hunziker, Markus, Littlejohn, Lance L., Sepanski, Mark R.
School: Baylor University
Department: Mathematics
School Location: United States -- Texas
Source: DAI-B 74/12(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Endomorphism ring, F[x], Finite, Local multiplication maps, Polynomial ring, Ring
Publication Number: 3593302
ISBN: 978-1-303-35890-6
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