# IJPAM: Volume 51, No. 1 (2009)

**ON SEPARABLE AND -SEPARABLE POLYNOMIALS**

OF DEGREE IN SKEW POLYNOMIAL RINGS

OF DEGREE 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: [email protected]

Department of Environmental and Mathematical Sciences

Faculty of Environmental Science and Technology

Okayama University

Tsushima, Okayama, 700-8530, JAPAN

e-mail: [email protected]

**Abstract.**Let be a ring with identity 1, a derivation of , and the skew polynomial ring such that
for each . Assume that is a ring of prime characteristic . Let
such that
. We study separability and -separablity of .

**Received: **January 23, 2009

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

**Key Words and Phrases: **-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