Roots of unity in definite quaternion orders

• Autorzy: Luis Arenas-Carmona
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R52: Quaternion and other division algebras: arithmetic, zeta functions
• 11S45: Algebras and orders, and their zeta functions
• 11R04: Algebraic numbers; rings of algebraic integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 4
• Strony: 381-393

Daty

wydano

2015

Twórcy

autor

Luis Arenas-Carmona

• Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

Identyfikatory

DOI

10.4064/aa170-4-5