This article is cited in 2 papers

RESEARCH ARTICLE

On the separability of the restriction functor

Th. Theohari-Apostolidi, H. Vavatsoulas

Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Abstract: Let $G$ be a group, $\Lambda=\bigoplus_{\sigma \in G}\Lambda_{\sigma}$ a strongly graded ring by $G$, $H$ a subgroup of $G$ and $\Lambda_{H}=\bigoplus_{\sigma\in H}\Lambda_{\sigma}$. We give a necessary and sufficient condition for the ring $\Lambda/\Lambda_{H}$ to be separable, generalizing the corresponding result for the ring extension $\Lambda/\Lambda_{1}$. As a consequence of this result we give a condition for $\Lambda$ to be a hereditary order in case $\Lambda$ is a strongly graded by finite group $R$-order in a separable $K$-algebra, for $R$ a Dedekind domain with quotient field $K$.

Keywords: separable algebras, strongly graded algebras, restriction functor, induction functor.

MSC: 16W50, 16G30, 16H05

Received: 12.05.2003
Revised: 23.10.2003

Language: English

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