A note on separable polynomials of degree 3 in skew polynomial rings

Shûichi Ikehata

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let B be a ring with identity 1, Z the center of B, D a derivation of B, and B[X; D] the skew polynomial ring such that αX = Xα + D(α) for each α ε B. Assume that 3 = 0 and Z is a semiprime ring. Let f = X3 -Xa -b ε B[X; D] such that f B[X; D] = B[X; D] f. Then we prove that f is a separable polynomial in B[X; D] if and only if there exits an element z in Z such that D2(z) -za = 1.

Original languageEnglish
Pages (from-to)145-149
Number of pages5
JournalInternational Journal of Pure and Applied Mathematics
Volume50
Issue number1
Publication statusPublished - Dec 1 2009

Keywords

  • Derivation
  • Separable polynomial
  • Skew polynomial ring

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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