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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154882 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862654849936523264 |
|---|---|
| author | Szeto, G. Lianyong Xue |
| author_facet | Szeto, G. Lianyong Xue |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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. 
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| first_indexed | 2025-12-02T01:26:13Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-154882 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T01:26:13Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Szeto, G. Lianyong Xue 2019-06-16T06:00:40Z 2019-06-16T06:00:40Z 2010 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. https://nasplib.isofts.kiev.ua/handle/123456789/154882 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 This paper was written under the support of a Caterpillar Fellowship at BradleyUniversity. The authors would like to thank Caterpillar Inc. for the support en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On separable group rings Article published earlier |
| spellingShingle | On separable group rings Szeto, G. Lianyong Xue |
| title | On separable group rings |
| title_full | On separable group rings |
| title_fullStr | On separable group rings |
| title_full_unstemmed | On separable group rings |
| title_short | On separable group rings |
| title_sort | on separable group rings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154882 |
| work_keys_str_mv | AT szetog onseparablegrouprings AT lianyongxue onseparablegrouprings |