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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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| 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 \(B\). |
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