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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ADM_2010_10_1_a9,
     author = {George Szeto and Lianyong Xue},
     title = {On separable group rings},
     journal = {Algebra and discrete mathematics},
     pages = {104--111},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a9/}
}
TY  - JOUR
AU  - George Szeto
AU  - Lianyong Xue
TI  - On separable group rings
JO  - Algebra and discrete mathematics
PY  - 2010
SP  - 104
EP  - 111
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a9/
LA  - en
ID  - ADM_2010_10_1_a9
ER  - 
%0 Journal Article
%A George Szeto
%A Lianyong Xue
%T On separable group rings
%J Algebra and discrete mathematics
%D 2010
%P 104-111
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a9/
%G en
%F ADM_2010_10_1_a9
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/