On q-Galois Extensions of Simple Rings

On Certain Classes of Galois Extensions of Rings

Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.

On a notion of “Galois closure” for extensions of rings

where a ∈ A and j ∈ {1, 2, . . . , n}. Note that the symmetric group Sn naturally acts on A⊗n by permuting the tensor factors, and the ideal I(A,B) ⊂ A⊗n is preserved under this Sn-action. We are interested in imposing on A⊗n the relations in I(A,B) defined by (2) because they are precisely the relations that the conjugates a(i) of a generic element a in a separable field extension of degree n ...

Semi-simple Extensions of Rings

In this paper we investigate the conditions under which a given ring is a sub-ring of a semi-simple ring. For convenience, we say that a ring A is an extension of a ring B, if B is a sub-ring of A. It is found that the existence of a semi-simple extension is equivalent to the vanishing of the extension radical, a two-sided ideal defined analogously to the ordinary radical. In Theorem II we give...

On Azumaya Galois Extensions and Skew Group Rings

Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois group.

Extensions of Nilpotent P.P. Rings