IJPAM: Volume 51, No. 1 (2009)

ON SEPARABLE AND $H$-SEPARABLE POLYNOMIALS
OF DEGREE $p$ IN SKEW POLYNOMIAL RINGS

Shûichi Ikehata
Department of Environmental and Mathematical Sciences
Faculty of Environmental Science and Technology
Okayama University
Tsushima, Okayama, 700-8530, JAPAN
e-mail: ikehata@ems.okayama-u.ac.jp


Abstract.Let $B$ be a ring with identity 1, $D$ a derivation of $B$, and $B[X;D]$ the skew polynomial ring such that $\alpha X = X\alpha + D(\alpha)$ for each $\alpha \in B$. Assume that $B$ is a ring of prime characteristic $p$. Let $f = X^p - Xa - b \in B[X;D]$ such that $fB[X;D] = B[X;D]f$. We study separability and $H$-separablity of $f$.

Received: January 23, 2009

AMS Subject Classification: 13N15, 16S32, 16W25

Key Words and Phrases: $H$-separable polynomial, skew polynomial ring, separable polynomial, derivation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 1