On the separability of the restriction functor

Th Theohari-Apostolidi, H Vavatsoulas
2003 Algebra and Discrete Mathematics RESEARCH ARTICLE Number   unpublished
Let G be a group, Λ = σ∈G Λ σ a strongly graded ring by G, H a subgroup of G and Λ H = σ∈H Λ σ. We give a necessary and sufficient condition for the ring Λ/Λ H to be separable, generalizing the corresponding result for the ring extension Λ/Λ 1. As a consequence of this result we give a condition for Λ to be a hereditary order in case Λ is a strongly graded by finite group R-order in a separable K-algebra, for R a Dedekind domain with quotient field K.