On separable abelian extensions of rings

[摘要] LetRbe a ring with1,G(=〈ρ1〉×…×〈ρm〉)a finite abelian automorphism group ofRof ordernwhere〈ρi〉is cyclic of orderni. for some integersn,ni, andm, andCthe center ofRwhose automorphism group induced byGis isomorphic withG. Then an abelian extensionR[x1,…,xm]is defined as a generalization of cyclic extensions of rings, andR[x1,…,xm]is an Azumaya algebra overK(=CG={c   in   C/(c)ρi=c   for each   ρi   in   G})such thatR[x1,…,xm]≅RG⊗KC[x1,…,xm]if and only ifCis Galois overKwith Galois groupG(the Kanzaki hypothesis).

[学科分类] 数学（综合）