Skew group rings which are azumaya

ON THE AZUMAYA LOCUS OF SOME CROSSED PRODUCTS#

“…Following the same ideas as the ones of S.Ikehata in [19], R.Alfaro and G. Szeto in [2], P. Carvalho in [9] or M. Ouyang in [28], we have the following general result. Proof.…”

“…In [19], Ikehata proves that given a commutative ring R and a finite group G of automorphisms of R, the skew-group ring R#G is an Azumaya R-algebra if and Following the aproach of Alfaro and Szeto in [2], in section 2 we consider crossed product of a ring R by any group J, R * J, such that Z(R * J) ⊆ R and describe when they are Azumaya in terms of H-separability. In section 3 we restrict ourselves to the crossed product of a ring R over a finite group acting faithfully on R and describe when R * G is H-separable using G-Galois extensions, Proposition 3.12.…”

On Hirata-Azumaya Galois extensions

“…In [5], [8], the class of Hirata separable and Galois extensions B of B G with Galois group G was investigated. In [1], [2], [14], the class of Galois extensions B of B G with Galois group G such that B G is an Azumaya C G -algebra was explored, such a B is called an Azumaya Galois extension. The purpose of the present paper is to study the class of Hirata separable and Azumaya Galois extensions B of B G with Galois group G. We shall show several characterizations of such a Galois extension B, and give an equivalent condition for such a B satisfying the fundamental theory which generalizes Theorem 3.4 in [10].…”

On certain classes of Galois extensions of rings

“…Recently, a class broader than classes (1) and (2) has been studied in [1,2], that is, the class of the Azumaya Galois extensions, where S is called an Azumaya G-Galois extension if it is a G-Galois extension of S G which is an Azumaya C G -algebra, where C is the center of S and G is a finite automorphism group of S. Moreover, properties of a Galois skew group ring of G over S and S * G were studied in [10]. Now, we continue the above investigation into the different types of Galois extensions of rings and also further study the properties of S * G. We define another two classes of Galois extensions containing all the Azumaya Galois extensions: (i) centrally projective Galois extension S, that is, S is G-Galois extension and centrally projective over S G (S is a direct summand of a finite direct sum of S G as a S G -bimodule),…”