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Algebra Discrete Math., 2010, Volume 10, Issue 1, Pages 104–111 (Mi adm43)  

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 $\overline G$ 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: Galois extensions, Galois algebras, separable extensions, group rings, group algebras.

Full text: PDF file (211 kB)

Bibliographic databases:
MSC: 16S35, 16W20
Received: 04.05.2009
Revised: 04.05.2009
Language:

Citation: George Szeto, Lianyong Xue, “On separable group rings”, Algebra Discrete Math., 10:1 (2010), 104–111

Citation in format AMSBIB
\Bibitem{SzeXue10}
\by George Szeto, Lianyong Xue
\paper On separable group rings
\jour Algebra Discrete Math.
\yr 2010
\vol 10
\issue 1
\pages 104--111
\mathnet{http://mi.mathnet.ru/adm43}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2807691}
\zmath{https://zbmath.org/?q=an:1212.16045}


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