### 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 = X^{3} -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 D^{2}(z) -za = 1.

Original language | English |
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Pages (from-to) | 145-149 |

Number of pages | 5 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 50 |

Issue number | 1 |

Publication status | Published - Dec 1 2009 |

### Keywords

- Derivation
- Separable polynomial
- Skew polynomial ring

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Ikehata, S. (2009). A note on separable polynomials of degree 3 in skew polynomial rings.

*International Journal of Pure and Applied Mathematics*,*50*(1), 145-149.