On the unit group of Z-orders in finite dimensional algebras
Connections between Algebra and Geometry: an introduction to Clifford algebras
Braids, configuration spaces and applications to multivalued maps
| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sao Paulo IME USP, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil
[2] Univ Sao Paulo EACH USP, Escola Artes Ciencias & Humanidades, BR-03828000 Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Algebra; v. 379, p. 314-321, APR 1 2013. |
| Web of Science Citations: | 2 |
| Abstract | |
In Juriaans et al. (2009) {[}9] we constructed pairs of units u, v in Z-orders of a quaternion algebra over Q(root-d), d a positive and square free integer with d equivalent to 7 (mod 8), such that (u(n), v(n)) is free for some n is an element of N. Here we extend this result to any imaginary quadratic extension of Q, thus including matrix algebras. More precisely, we show that < u(n), v(n)> is a free group for all n >= 1 and d > 2 and for d = 2 and all n >= 2. The units we use arise from Pell's and Gauss' equations. (C) 2013 Elsevier Inc. All rights reserved. (AU) | |