Geodesic
On separable group rings
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 104-111

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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.
Keywords: separable extensions, group rings
Mots-clés : Galois extensions, Galois algebras, group algebras. 
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     author = {George Szeto and Lianyong Xue},
     title = {On separable group rings},
     journal = {Algebra and discrete mathematics},
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     volume = {10},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a9/}
}
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George Szeto; Lianyong Xue. On separable group rings. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 104-111. http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a9/