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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 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
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}