Geodesic
On the separability of the restriction functor
Algebra and discrete mathematics, no. 3 (2003), pp. 95-101.

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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. 
@article{ADM_2003_3_a6,
     author = {Th. Theohari-Apostolidi and H. Vavatsoulas},
     title = {On the separability of the restriction functor},
     journal = {Algebra and discrete mathematics},
     pages = {95--101},
     publisher = {mathdoc},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_3_a6/}
}
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Th. Theohari-Apostolidi; H. Vavatsoulas. On the separability of the restriction functor. Algebra and discrete mathematics, no. 3 (2003), pp. 95-101. http://geodesic.mathdoc.fr/item/ADM_2003_3_a6/