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This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that

factors into linear factors over $K$,

This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that

factors into linear factors over $K$, as do all of its derivatives. Such a polynomial

is said to be {\it proper} if

its roots are distinct. An unresolved question in the literature is

whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples

are known of proper $K$-derived quartics for a quadratic number field $K$, although other

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Date Created
  • 2019
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  • Text
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    Note
    • Partial requirement for: Ph.D., Arizona State University, 2019
      Note type
      thesis
    • Includes bibliographical references (pages 2603-2605)
      Note type
      bibliography
    • Field of study: Mathematics

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    by Benjamin Carrillo

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