Galois extensions
On certain classes of Galois extensions of rings
... of Galois extensions are given: (1) cen- trally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable ...
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On central commutator Galois extensions of rings
... commutator Galois extension in terms of Galois H- separable extensions and Azumaya Galois extensions, respectively, and prove the converse of a theorem for a Galois H-separable ...
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On Hopf DeMeyer Kanzaki Galois extensions
... Azumaya Galois extensions of a ring as studied in [1, 2] was generalized to H ∗ -Azumaya Galois ...-Azumaya Galois extension B was char- acterized in terms of the smash product B # H see [7, ...
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On weak center Galois extensions of rings
... [6] S. Ikehata and G. Szeto, On H-skew polynomial rings and Galois extensions, Rings, Exten- sions, and Cohomology (Evanston, IL, 1993) (A. R. Magid, ed.), Lecture Notes in Pure and Appl. Math., vol. 159, ...
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The Galois extensions induced by idempotents in a Galois algebra
... a Galois extension with Galois group G(e) for a central idempotent e of B if and only if B = Be ⊕ B(1− e) such that Be and B(1− e) are Galois extensions with Galois group induced by and ...
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Modularity of residual Galois extensions and the Eisenstein ideal
... corresponding modular extensions (arising from Eisenstein congruences). Hence it can be viewed as in some sense ensuring an abundance of reducible modular deformations of appropriate type. Roughly speaking, the ...
23
On Azumaya Galois extensions and skew group rings
... [1] R. Alfaro and G. Szeto, The centralizer on H-separable skew group rings, Rings, extensions, and cohomology (New York), Lecture Notes in Pure and Appl. Math., vol. 159, Marcel Dekker, Inc., 1994, Basal Hong ...
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GENERIC GALOIS EXTENSIONS FOR FAMILIES OF FINITE GROUPS
... for any finite group G and any field k, there does not always exist a generic Galois extension for G over k. However, we have shown that there always exists a G-Galois extension S'/R' [r] ...
79
The Galois algebras and the Azumay Galois extensions
... a Galois algebra over a commutative ring R with Galois group G, C the center of B, K = { g ∈ G | g(c) = c for all c ∈ C }, J g = { b ∈ B | bx = g(x)b for all x ∈ B } for each g ∈ K, and B K = ( ⊕ g∈K J g ...
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On separable group rings
... Galois extensions for rings and Hopf algebras have been intensively in- vestigated ([3], [7], [8], [10], [11]) and many examples are ...a Galois algebra? In [3], it was shown that any Azumaya ...
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Galois 2-Extensions
... all Galois extensions L/F whose Galois groups are isomorphic to group ...of extensions using invariants of L/F which depend only on the base field ...of Galois extensions L/F ...
105
Noncommutative principal bundles through twist deformation
... The outline of the paper is the following: in § 2.1 we recall the basic definitions and results about Hopf-Galois extensions, while in §2.2 we review some results from the theory of deformations of Hopf ...
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GALOIS E X T E N S I O N S R A MI FI E DA TO N EP R I ME
... studies Galois extensions of global fields and associated Galois groups with one ramified prime, in both the number field and function field ...nonsolvable Galois groups ramified only at one ...
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LOCAL EXTENSIONS WITH IMPERFECT RESIDUE FIELD
... Let K be any CDVF of characteristic p > 0 with no special assumption on K, the residue field of K. Write G(p) for the biggest quotient of G which is a pro-p-group. G(p) is the Galois group of the maximal ...
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Cohomology of Absolute Galois Groups
... the Galois groups of infinite Galois extensions of fields, as such groups are profinite groups, and they carry with them a natural topology, the Krull topology, which is induced by the Galois ...
120
On free ring extensions of degree n
... In this section, we shall show that if Bx is an Azumaya A-algebra in which b and n are units, then Ax is a splitting ring for Bx such that Ax is a chain of Galois extensions of degree 2 [r] ...
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Miguel Ferrero
... dihedral Galois extensions (with ...ring extensions, their prime ideals, radicals and automorphisms, as well as distributivity in rings and modules and derivations of rings, became also main streams ...
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... finite Galois p-extensions of local ...the Galois extensions of a local field having a given Galois group G requires knowledge of the character table of G as well as its ...
128
On Galois 2-extensions of the Dihedral Group.
... be able to reduce the computation of the obstruction to a computation of quadratic forms of ` Etale algerbas. And in so doing we obtain the obstruction formula due to Serre. This formula reduces the solvability of the ...
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On separable abelian extensions of rings
... Abelian ring extensions, separable algebras, Azumaya.. algebras, Galois extensions..[r] ...
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