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- Title
A Characterization of Central Galois Algebras.
- Authors
Xiao-Long Jiang; Szeto, George
- Abstract
Let A be an Azumaya R-algebra over a commutative ring R of a constant rank n for some integer n, G an automorphism group of A of order n, and Jg = {a ∈ A|ax = g(x)a for all x ∈ A} for g ∈ G. Then A is a central Galois algebra over R with Galois group G if and only if ∑g∈Gg is a separable R-algebra of rank n. In particular, when G is inner induced by {Ug for g ∈ G}, A is a central Galois R-algebra if and only if ∑g RUg is a separable R-algebra of rank n. Thus all inner Galois groups can be computed from the multiplicative group of units of A.
- Subjects
AZUMAYA algebras; COMMUTATIVE rings; INTEGERS; AUTOMORPHISMS; GALOIS theory
- Publication
General Mathematics Notes, 2014, Vol 23, Issue 2, p11
- ISSN
2219-7184
- Publication type
Article