On separable and \(H\)-separable polynomials in skew polynomial rings of several variables

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,...

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Bibliographische Detailangaben
Datum:2018
1. Verfasser: Ikehata, Shuichi
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
Beschreibung
Zusammenfassung: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 \(B\).