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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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