On free subgroups of units in quaternion algebras II

Jan Krempa. "On free subgroups of units in quaternion algebras II." Colloquium Mathematicae 97.1 (2003): 29-32. <http://eudml.org/doc/285310>.

@article{JanKrempa2003,
abstract = {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.},
author = {Jan Krempa},
journal = {Colloquium Mathematicae},
keywords = {Cayley algebras; groups of units; free groups; Tits alternative; quaternion rings},
language = {eng},
number = {1},
pages = {29-32},
title = {On free subgroups of units in quaternion algebras II},
url = {http://eudml.org/doc/285310},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Jan Krempa
TI - On free subgroups of units in quaternion algebras II
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 1
SP - 29
EP - 32
AB - 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.
LA - eng
KW - Cayley algebras; groups of units; free groups; Tits alternative; quaternion rings
UR - http://eudml.org/doc/285310
ER -