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.
|Number of pages||5|
|Journal||International Journal of Pure and Applied Mathematics|
|Publication status||Published - Dec 1 2009|
- Separable polynomial
- Skew polynomial ring
ASJC Scopus subject areas
- Applied Mathematics