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Title :HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS
Authors :Yamashiro, Yasukazu
Authors alternative :山城, 康一
Issue Date :Dec-2011
Abstract :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]).
Type Local :紀要論文
ISSN :1344-008X
Publisher :Department of Mathematical Science, Faculty of Science, University of the Ryukyus
URI :http://hdl.handle.net/20.500.12000/23607
Citation :Ryukyu mathematical journal Vol.24 p.117 -121
Appears in Collections:Vol.24 (2011)

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