On free subgroups of units in quaternion algebras II

• Autorzy: Jan Krempa
• Języki publikacji: EN

Abstrakty

EN

Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.

Kategorie tematyczne

• 16U60: Units, groups of units
• 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
• 11D57: Multiplicative and norm form equations
• 17D05: Alternative rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 1
• Strony: 29-32

Daty

wydano

2003

Twórcy

autor

Jan Krempa

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

Identyfikatory

DOI

10.4064/cm97-1-4