On free subgroups of units in quaternion algebras

• Autorzy: Jan Krempa
• Języki publikacji: EN

Abstrakty

EN

It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments as simple as possible.

Kategorie tematyczne

• 16U60: Units, groups of units
• 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
• 11A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 88
• Numer: 1
• Strony: 21-27

Daty

wydano

2001

Twórcy

autor

Jan Krempa

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm88-1-3