On certain classes of Galois extensions of rings. (English) Zbl 1005.16025

Szeto, George; Xue, Lianyong

Int. J. Math. Math. Sci. 25, No. 5, 315-321 (2001).

The aim of this paper is to investigate relations between the following classes of Galois extensions of noncommutative rings: centrally projective Galois extensions, faithfully Galois extensions, and \(H\)-separable Galois extensions. It is shown that the intersection of the class of centrally projective Galois extensions and the class of faithfully Galois extensions is precisely the class Azumaya Galois extensions.

Reviewer: Toma Albu (Ankara)

MSC:

16S35	Twisted and skew group rings, crossed products
16W20	Automorphisms and endomorphisms
16H05	Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16W22	Actions of groups and semigroups; invariant theory (associative rings and algebras)

Keywords:

Galois extensions of noncommutative rings; centrally projective Galois extensions; faithfully Galois extensions; \(H\)-separable Galois extensions; Azumaya Galois extensions