Polynomials and Vandermonde matrices over the field of quaternions.
Potenzen von Galoisfeldern.
Prime factorization of integral Cayley octaves
Quadratische Semi-Ordnungen und Quadratische Formen.
Quaternions et
Quelques remarques sur le cas sauvage.
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition
In this paper, first we introduce a new notion of commuting condition that between the shape operator and the structure tensors and for real hypersurfaces in . Suprisingly, real hypersurfaces of type , that is, a tube over a totally geodesic in complex two plane Grassmannians satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in satisfying the commuting condition. Finally we get a characterization of Type in terms of such commuting...
Relative Brauer Groups. I.
Relative Brauer groups. III.
Representation fields for commutative orders
A representation field for a non-maximal order in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of . Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.
Representation fields for cyclic orders
Roots of unity in definite quaternion orders
A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with type number 3 or larger. The proof extends to a few other closely related orders.
Rotations in the space of Split octonions.
Signatures of fields and extension theory.
Simplification pour les ordres des corps de quaternions totalement définis.
Small zeros of hermitian forms over a quaternion algebra
Solomon's Zeta Functions over Algebraic Function Fields.
Some counter-examples in the theory of the Galois module structure of wild extensions
Considering the ring of integers in a number field as a -module (where is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.
Some Invariants of Zd-p-Extensions.
Some properties of orders of quaternion algebras with regard to the discrete norm
Quaternion algebras are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.