A generalization of the primitive normal basis theorem

Chih Nung Hsu*, Ting Ting Nan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The primitive normal basis theorem asks whether every finite field extension has a primitive normal basis of this extension. The proof of this problem has recently been completed by Lenstra and Schoof (1987) [6], and another proof is given by Cohen and Huczynska (2003) [3]. We present a more general result, where the primitive element generating a normal basis is replaced by a primitive element generating the finite Carlitz module. Such generators always exist except for finitely many cases which might not exist.

Original languageEnglish
Pages (from-to)146-157
Number of pages12
JournalJournal of Number Theory
Issue number1
Publication statusPublished - 2011 Jan


  • Character sum over finite fields
  • Finite Carlitz modules
  • Primitive roots

ASJC Scopus subject areas

  • Algebra and Number Theory


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