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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2010, Volume 10, Issue 2, Pages 87–96 (Mi adm50)

RESEARCH ARTICLE

On separable and $H$-separable polynomials in skew polynomial rings of several variables

Sh. Ikehata

Department of Environmental and Mathematical Science, Faculty of Environmental Science and Technology, Okayama University, Tsushima, Okayama 700-8530, Japan

Abstract: Let $B$ be a ring with 1, and $\{\rho_1,\cdots,\rho_e\}$ a set of automorphisms of $B$. Let $B[X_1, \cdots,X_e;\rho_1,\cdots,\rho_e;\{ u_{ij}\}]$ be the skew polynomial ring of automorphism type. In this paper, we shall give equivalent conditions that the residue ring of $B[X_1,\cdots,X_e;\rho_1,\cdots,\rho_e;\{ u_{ij}\}]$ by the ideal generated by a set $\{X_1^{m_1}-u_1,\cdots,X_e^{m_e}-u_e\}$ to be separable or $H$-separable over $B$.

Keywords: $H$-separable polynomial, separable extension, skew polynomial ring.

Full text: PDF file (219 kB)

Bibliographic databases:
UDC: 16S30, 16W20
Revised: 28.02.2011
Language:

Citation: Sh. Ikehata, “On separable and $H$-separable polynomials in skew polynomial rings of several variables”, Algebra Discrete Math., 10:2 (2010), 87–96

Citation in format AMSBIB
\Bibitem{Ike10} \by Sh.~Ikehata \paper On separable and $H$-separable polynomials in skew polynomial rings of several variables \jour Algebra Discrete Math. \yr 2010 \vol 10 \issue 2 \pages 87--96 \mathnet{http://mi.mathnet.ru/adm50} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884745} \zmath{https://zbmath.org/?q=an:1212.16050}