Tame and Galois extensions with respect to Hopf orders.
Tame orders
Tentative de description immobilière de quelques représentations intégrales de groupes finis (avec l'aide de Guy Rousseau)
Th normal decomposition of lattices and the Krull-Schmidt theorem.
The atomicity of a "lattice" of hereditary annihilator torsions
The Brauer and Brauer-Taylor groups of a symmetric monoidal category
The Brauer ring of a commutative ring
The Class Number of Hereditary Orders in Non-Eichler Algebras over Global Fuction Fields.
The existence of Galois sets
The Galois algebras and the Azumaya Galois extensions.
The Galois extensions induced by idempotents in a Galois algebra.
The general Ikehata theorem for -separable crossed products.
The invariant subrings of DeMeyer-Kanzaki Galois extensions.
The Prime Ideal Theorem in Non-Commutative Arithmetic.
Topological Hochschild cohomology and generalized Morita equivalence.
Totally indefinite Euclidean quaternion fields
We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
Twists of Central Simple Algebras and Endomorphism Algebras of Some Abelian Varieties.
Two-dimensional orders of finite representation type.