<p>For a field <i>F</i> and the polynomial ring <i>F</i> [<i>x</i>] in a single indeterminate, we define [special characters omitted] = {α ∈ End<i><sub>F</sub></i>(<i>F</i> [x]) : α(<i>f</i>) ∈ <i>f F</i> [<i>x </i>] for all <i>f</i> ∈ <i>F</i> [<i> x</i>]}. Then [special characters omitted] is naturally isomorphic to <i>F</i> [<i>x</i>] if and only if <i>F</i> is infinite. If <i>F</i> is finite, then [special characters omitted] has cardinality continuum. We study the ring [special characters omitted] for finite fields <i>F.</i> For the case that <i>F </i> is finite, we discuss many properties and the structure of [special characters omitted].</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3593302 |
| Date | 15 October 2013 |
| Creators | Fouts, Kelly Jean |
| Publisher | Baylor University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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