On separable group rings
Let G be a finite non-abelian group, R a ring with 1, and Ĝ 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)Ĝ with Galois group Ĝ when the order of...
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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154882 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On separable group rings / G. Szeto, Lianyong Xue // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 104–111. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-154882 |
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irk-123456789-1548822019-06-17T01:31:29Z On separable group rings Szeto, G. Lianyong Xue Let G be a finite non-abelian group, R a ring with 1, and Ĝ 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)Ĝ with Galois group Ĝ 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. Remove selected 2010 Article On separable group rings / G. Szeto, Lianyong Xue // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 104–111. — Бібліогр.: 13 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16S35, 16W20. http://dspace.nbuv.gov.ua/handle/123456789/154882 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let G be a finite non-abelian group, R a ring with 1, and Ĝ 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)Ĝ with Galois group Ĝ 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.
Remove selected |
| format |
Article |
| author |
Szeto, G. Lianyong Xue |
| spellingShingle |
Szeto, G. Lianyong Xue On separable group rings Algebra and Discrete Mathematics |
| author_facet |
Szeto, G. Lianyong Xue |
| author_sort |
Szeto, G. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154882 |
| citation_txt |
On separable group rings / G. Szeto, Lianyong Xue // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 104–111. — Бібліогр.: 13 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT szetog onseparablegrouprings AT lianyongxue onseparablegrouprings |
| first_indexed |
2023-05-20T17:45:27Z |
| last_indexed |
2023-05-20T17:45:27Z |
| _version_ |
1796154014585323520 |