Square-free criteria for polynomials using no derivatives

E. Alkan, A. I. Bonciocat, N. C. Bonciocat, A. Zaharescu

Research output: Contribution to journalArticlepeer-review


We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce squarefree criteria for polynomials in several variables.

Original languageEnglish (US)
Pages (from-to)677-687
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 2007


  • Frobenius map
  • Primitive polynomials
  • Resultants
  • Square-free criteria

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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