Geodesic
On separable and $H$-separable polynomials in skew polynomial rings of several variables
Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 87-96.

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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. 
@article{ADM_2010_10_2_a6,
     author = {Sh. Ikehata},
     title = {On separable and $H$-separable polynomials in skew polynomial rings of several variables},
     journal = {Algebra and discrete mathematics},
     pages = {87--96},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a6/}
}
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Sh. Ikehata. On separable and $H$-separable polynomials in skew polynomial rings of several variables. Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 87-96. http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a6/