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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543157786771456 |
|---|---|
| author | Ikehata, Shuichi |
| author_facet | Ikehata, Shuichi |
| author_sort | Ikehata, Shuichi |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:17:05Z |
| 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 \(B\). |
| first_indexed | 2025-12-02T15:36:30Z |
| format | Article |
| id | admjournalluguniveduua-article-652 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:36:30Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| 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 |
| title | 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_short | 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 |
| topic | \(H\)-separable polynomial separable extension skew polynomial ring 16S30 16W20 |
| topic_facet | \(H\)-separable polynomial separable extension skew polynomial ring 16S30 16W20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/652 |
| work_keys_str_mv | AT ikehatashuichi onseparableandhseparablepolynomialsinskewpolynomialringsofseveralvariables |