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Algebra and Discrete Mathematics, 2010, Volume 10, Issue 1, Pages 104–111
(Mi adm43)
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RESEARCH ARTICLE
On separable group rings
George Szeto, Lianyong Xue Department of Mathematics, Bradley University, Peoria, Illinois 61625-U.S.A.
Abstract:
Let G be a finite non-abelian group R a ring with 1, and ¯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)¯G with Galois group ¯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.
Keywords:
Galois extensions, Galois algebras, separable extensions, group rings, group algebras.
Received: 04.05.2009 Revised: 04.05.2009
Citation:
George Szeto, Lianyong Xue, “On separable group rings”, Algebra Discrete Math., 10:1 (2010), 104–111
Linking options:
https://www.mathnet.ru/eng/adm43 https://www.mathnet.ru/eng/adm/v10/i1/p104
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Abstract page: | 146 | Full-text PDF : | 96 | References: | 5 | First page: | 1 |
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