Normal bases for infinite Galois ring extensions
On a notion of “Galois closure” for extensions of rings
We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an degree extension of fields. Moreover, we prove a number of properties of this construction; for example, we show that it is functorial and respects base change. We also investigate the behavior of this Galois closure construction for various natural classes of ring extensions.
On abelian separable extensions and Galois sets of rings
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On finitely generated birational flat extensions of integral domains
On generalized quaternion algebras.
On Prime Ideals in Representation Rings.
On Separable Subalgebras of Azumaya Algebras
On the Galois structure of the square root of the codifferent
Let be a finite abelian extension of , with the ring of algebraic integers of . We investigate the Galois structure of the unique fractional -ideal which (if it exists) is unimodular with respect to the trace form of .
On the geometrization of a lemma of Singer and van der Put
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory, used by Singer and van der Put in their reference book. This geometrization, in addition of giving a nice insight on this result, offers us the opportunity to investigate several points of differential algebra and differential algebraic geometry. We study the class of simple Δ-schemes and prove that they all have a coarse space of leaves. Furthermore, instead of considering schemes endowed with...
Polynomials with minimal value set over Galois rings.
Primitive elements in rings of holomorphic functions.
Self-dual normal bases for infinite odd abelian Galois ring extensions
Sur deux conjectures de Small
Sur la cohomologie des formes quadratiques
Sur les objets profinis et progénérateurs dans les catégories fermées
The factorization of the derivative of Dickson polynomials.
The intersection of distinct Galois subrings is not necessarily Galois
The local lifting problem for actions of finite groups on curves
Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB obstruction...
The reflectiveness of covering morphisms in algebra and geometry.