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

Shûichi Ikehata

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

Shûichi Ikehata

Research output: Contribution to journal › Article › peer-review

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 language	English
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

Cite this

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N2 - 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.

AB - 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.

KW - Derivation

KW - Separable polynomial

KW - Skew polynomial ring

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JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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