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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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-6522018-04-04T09:17:05Z On separable and \(H\)-separable polynomials in skew polynomial rings of several variables Ikehata, Shuichi \(H\)-separable polynomial, separable extension, skew polynomial ring 16S30, 16W20 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 \(B\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652/186 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-04T09:17:05Z |
| collection |
OJS |
| language |
English |
| topic |
\(H\)-separable polynomial separable extension skew polynomial ring 16S30 16W20 |
| spellingShingle |
\(H\)-separable polynomial separable extension skew polynomial ring 16S30 16W20 Ikehata, Shuichi On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| topic_facet |
\(H\)-separable polynomial separable extension skew polynomial ring 16S30 16W20 |
| format |
Article |
| author |
Ikehata, Shuichi |
| author_facet |
Ikehata, Shuichi |
| author_sort |
Ikehata, Shuichi |
| title |
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| title_short |
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| title_full |
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| title_fullStr |
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| title_full_unstemmed |
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables |
| title_sort |
on separable and \(h\)-separable polynomials in skew polynomial rings of several variables |
| description |
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 \(B\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 |
| work_keys_str_mv |
AT ikehatashuichi onseparableandhseparablepolynomialsinskewpolynomialringsofseveralvariables |
| first_indexed |
2025-12-02T15:36:30Z |
| last_indexed |
2025-12-02T15:36:30Z |
| _version_ |
1850411361557807104 |