HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS2011 · In [5], we considered the equivalent class of desending chains of subrings. In this note, we consider Hirata separable extension (H-separable extension) over the desending chain of subrings. Let Λ be a ring, Γ a subring of Λ, C the center of Λ and Δ the commutater of Γ in Λ. Λ is a Hirata separabale extension over Γ if and only if Δ is C-finitely generated projective and Λ ?_γ Λ ? Hom_c(Δ , Λ) by the map a ? b → [d → adb], where a ? b ∈ Λ ?_γ Λ and d ∈ Δ (Theorem 1.1 in [3]). （管理者追加）リポジトリ登録情報を移行しました。確認のうえ、加除修正をしてください。
