带内Galois群的Galois扩张

Galois Extensions with Inner Galois Groups

本文在Azumaya代数的条件下,对一般的带内Galois群的Galois扩张的结构进行了刻划。

Suppose that ring A is a Galois extension over its subring B, with finiteinner Galois group G. The main result of this paper is as follows: If (1) A is an AzumayaC -Algebra,and (2) C. Gf is an Azumaya C-Algebra (or eguivalently, n∈U (C) and C·Gf∩B=C) then A≌C·Gf?cA^G such that A^G is an Azumaya C-Algebra, where C is the center of A, U(C)the units of C, C·Gf the projective group algebra of Gover C, with factor set f: G×G→U(C). Moreover, the corresponding converse theorem is also given.