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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 f ∈ F [ 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].
| 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 |
| Source Type: | DISSERTATION |
| 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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