# IJPAM: Volume 50, No. 1 (2009)

**A NOTE ON SEPARABLE POLYNOMIALS OF DEGREE**

IN SKEW POLYNOMIAL RINGS

IN SKEW POLYNOMIAL RINGS

Shûichi Ikehata

Department of Environmental and Mathematical Science

Faculty of Environmental Science and Technology

Okayama University

Tsushima, Okayama 700-8530, JAPAN

e-mail: ikehata@ems.okayama-u.ac.jp

Department of Environmental and Mathematical Science

Faculty of Environmental Science and Technology

Okayama University

Tsushima, Okayama 700-8530, JAPAN

e-mail: ikehata@ems.okayama-u.ac.jp

**Abstract.**Let be a ring with identity 1, the center of , a derivation of , and the skew polynomial ring such that
for each . Assume that and is a semiprime ring. Let
such that
. Then we prove that is a separable polynomial in if and only if there exits an element in such that
.

**Received: **December 26, 2008

**AMS Subject Classification: **16S30, 16W20

**Key Words and Phrases: **separable polynomial, skew polynomial ring, derivation

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 50

**Issue:** 1