HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS

概要

論文の詳細を見る
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]).