### Abstract

Let B be a ring with identity 1, D a derivation of B, and B[X; D] the skew polynomial ring such that αX = Xα + D(α) for each a S B. Assume that B is a ring of prime characteristic p. Let f = X^{p} -Xa -b ∈ B[X; D] such that f B[X; D] = B[X; D] f. We study separability and H-separablity of f.

Original language | English |
---|---|

Pages (from-to) | 149-156 |

Number of pages | 8 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 51 |

Issue number | 1 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Derivation
- H-separable polynomial
- Separable polynomial
- Skew polynomial ring

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*International Journal of Pure and Applied Mathematics*,

*51*(1), 149-156.

**On separable and H-separable polynomials of degree p in skew polynomial rings.** / Ikehata, ShÛichi.

Research output: Contribution to journal › Article

*International Journal of Pure and Applied Mathematics*, vol. 51, no. 1, pp. 149-156.

}

TY - JOUR

T1 - On separable and H-separable polynomials of degree p in skew polynomial rings

AU - Ikehata, ShÛichi

PY - 2009

Y1 - 2009

N2 - Let B be a ring with identity 1, D a derivation of B, and B[X; D] the skew polynomial ring such that αX = Xα + D(α) for each a S B. Assume that B is a ring of prime characteristic p. Let f = Xp -Xa -b ∈ B[X; D] such that f B[X; D] = B[X; D] f. We study separability and H-separablity of f.

AB - Let B be a ring with identity 1, D a derivation of B, and B[X; D] the skew polynomial ring such that αX = Xα + D(α) for each a S B. Assume that B is a ring of prime characteristic p. Let f = Xp -Xa -b ∈ B[X; D] such that f B[X; D] = B[X; D] f. We study separability and H-separablity of f.

KW - Derivation

KW - H-separable polynomial

KW - Separable polynomial

KW - Skew polynomial ring

UR - http://www.scopus.com/inward/record.url?scp=78649765023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649765023&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78649765023

VL - 51

SP - 149

EP - 156

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

SN - 1311-8080

IS - 1

ER -