On separable group rings
Let \(G\) be a finite non-abelian group, \(R\) a ring with 1, and \(\overline G\) the inner automorphism group of the group ring \(RG\) over \(R\) induced by the elements of \(G\). Then three main results are shown for the separable group ring \(RG\) over \(R\): (i) \(RG\) is not a Galois extension...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/645 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-645 |
|---|---|
| record_format |
ojs |
| spelling |
admjournalluguniveduua-article-6452018-04-04T09:14:15Z On separable group rings Szeto, George Xue, Lianyong Galois extensions, Galois algebras, separable extensions, group rings, group algebras 16S35, 16W20 Let \(G\) be a finite non-abelian group, \(R\) a ring with 1, and \(\overline G\) the inner automorphism group of the group ring \(RG\) over \(R\) induced by the elements of \(G\). Then three main results are shown for the separable group ring \(RG\) over \(R\): (i) \(RG\) is not a Galois extension of \((RG)^{\overline G}\) with Galois group \(\overline G\) when the order of \(G\) is invertible in \(R\), (ii) an equivalent condition for the Galois map from the subgroups \(H\) of \(G\) to \((RG)^{H}\) by the conjugate action of elements in \(H\) on \(RG\) is given to be one-to-one and for a separable subalgebra of \(RG\) having a preimage, respectively, and (iii) the Galois map is not an onto map. 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/645 Algebra and Discrete Mathematics; Vol 10, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/645/179 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:14:15Z |
| collection |
OJS |
| language |
English |
| topic |
Galois extensions Galois algebras separable extensions group rings group algebras 16S35 16W20 |
| spellingShingle |
Galois extensions Galois algebras separable extensions group rings group algebras 16S35 16W20 Szeto, George Xue, Lianyong On separable group rings |
| topic_facet |
Galois extensions Galois algebras separable extensions group rings group algebras 16S35 16W20 |
| format |
Article |
| author |
Szeto, George Xue, Lianyong |
| author_facet |
Szeto, George Xue, Lianyong |
| author_sort |
Szeto, George |
| title |
On separable group rings |
| title_short |
On separable group rings |
| title_full |
On separable group rings |
| title_fullStr |
On separable group rings |
| title_full_unstemmed |
On separable group rings |
| title_sort |
on separable group rings |
| description |
Let \(G\) be a finite non-abelian group, \(R\) a ring with 1, and \(\overline G\) the inner automorphism group of the group ring \(RG\) over \(R\) induced by the elements of \(G\). Then three main results are shown for the separable group ring \(RG\) over \(R\): (i) \(RG\) is not a Galois extension of \((RG)^{\overline G}\) with Galois group \(\overline G\) when the order of \(G\) is invertible in \(R\), (ii) an equivalent condition for the Galois map from the subgroups \(H\) of \(G\) to \((RG)^{H}\) by the conjugate action of elements in \(H\) on \(RG\) is given to be one-to-one and for a separable subalgebra of \(RG\) having a preimage, respectively, and (iii) the Galois map is not an onto map. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/645 |
| work_keys_str_mv |
AT szetogeorge onseparablegrouprings AT xuelianyong onseparablegrouprings |
| first_indexed |
2025-12-02T15:43:03Z |
| last_indexed |
2025-12-02T15:43:03Z |
| _version_ |
1850411774341283840 |