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A generalization of Eichler's trace formula.
Eichler's trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.
A note on Skolem-Noether algebras
The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let be a unital commutative ring, not necessarily a field. Given a unital -algebra , where is contained in the center of , , the goal of this paper is to study the question: when can a homomorphism be extended to an inner automorphism of ? As an application of main results presented in the paper, it is proved that if is a semilocal...
À propos d'un théorème de Frobenius
A question on the discriminants of involutions of central division algebras.
A weak Hasse principle for central simple algebras with an involution.
An application of Zassenhaus' unit theorem
Biquaternion algebras and quartic extensions
Certain simple maximal subfields in division rings
Let be a division ring finite dimensional over its center . The goal of this paper is to prove that for any positive integer there exists the th multiplicative derived subgroup such that is a maximal subfield of . We also show that a single depth- iterated additive commutator would generate a maximal subfield of
Cohomological approaches to and of central simple algebras.
Completely O-simple multiplicative ideals of rings.
Constructions and homological properties of simple von Neumann regular rings
Corestriction of central simple algebras and families of Mumford-type
Let be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra over a real cubic number field and imposing a condition to the corestriction of such . In this paper, under some extra conditions on the algebra , we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple -fibers...
Decomposition of Mal'cev-Neumann division algebras with involution.
Division algebras that ramify only along a singular plane cubic curve.
Ein Satz zur Galoistheorie in Schiefkörpern.
Elements of Quaternions [Book]
Existence of pseudo-superinvolutions of the first kind.
Homology of maximal orders in central simple algebras.
Hyperbolic involutions.