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A generalization of Eichler's trace formula.

Juliusz Brzezinski (1997)

Collectanea Mathematica

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

Juncheol Han, Tsiu-Kwen Lee, Sangwon Park (2021)

Czechoslovak Mathematical Journal

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 K be a unital commutative ring, not necessarily a field. Given a unital K -algebra S , where K is contained in the center of S , n ∈ ℕ , the goal of this paper is to study the question: when can a homomorphism φ : M n ( K ) → M n ( S ) be extended to an inner automorphism of M n ( S ) ? As an application of main results presented in the paper, it is proved that if S is a semilocal...

Certain simple maximal subfields in division rings

Mehdi Aaghabali, Mai Hoang Bien (2019)

Czechoslovak Mathematical Journal

Let D be a division ring finite dimensional over its center F . The goal of this paper is to prove that for any positive integer n there exists a ∈ D ( n ) , the n th multiplicative derived subgroup such that F ( a ) is a maximal subfield of D . We also show that a single depth- n iterated additive commutator would generate a maximal subfield of D .

Corestriction of central simple algebras and families of Mumford-type

Federica Galluzzi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let M 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 A over a real cubic number field and imposing a condition to the corestriction of such A . In this paper, under some extra conditions on the algebra A , 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 C ⁢ M -fibers...

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