环的Galois、分离和Frobenius扩张

On Galois,Separable and Frobenins Extensions of Rings

设∧是其中心Ｃ＿∧上的有限维单代数，Ｆ是满足Ｃ＿∧的∧的子环，Ｇ是保持Γ的元素不变的∧的自同构的有限群．本文证明：若∧／Γ是Ｇ－Ｇａｌｏｉｓ扩张，则在∧中的中心化子△是Ｃ＿Γ一分离代数且∧／Γ是Ｆｒｏｂｅｎｉｕｓ扩张，这里Ｃ＿Γ是Γ的中心．

Let∧be a finite dimensional simple algebra over its centerC_∧,C_∧ and G be a finite group of automorphisms of∧leavingГelementwise fixed.In this paper it is shown that if∧/Гis a G-Galois extension,then the centralizer △ of in∧is a separableC_Гalgebra and ∧/Гis a Frobenius extension,where C_Гis the center of Г.