| Title:
|
Some properties of orders of quaternion algebras with regard to the discrete norm (English) |
| Author:
|
Horníček, Jan |
| Author:
|
Kureš, Miroslav |
| Author:
|
Macálková, Lenka |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
385-405 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Quaternion algebras $(\frac {-1,b}{\mathbb {Q}})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved. (English) |
| Keyword:
|
order in an imaginary quadratic field |
| Keyword:
|
order in a quaternion algebra |
| Keyword:
|
discretely normed ring |
| Keyword:
|
isomorphism |
| Keyword:
|
primitive algebra |
| MSC:
|
11R52 |
| MSC:
|
16H05 |
| MSC:
|
16H20 |
| idZBL:
|
Zbl 06644020 |
| idMR:
|
MR3557586 |
| DOI:
|
10.21136/MB.2016.0026-15 |
| . |
| Date available:
|
2016-10-01T16:04:32Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145900 |
| . |
| Reference:
|
[1] Cohn, P. M.: On the structure of the {$ GL_2$} of a ring.Publ. Math., Inst. Hautes Études Sci. Publ. Math. 30 (1966), 5-53. MR 0207856, 10.1007/BF02684355 |
| Reference:
|
[2] James, D. G.: Quaternion algebras, arithmetic Kleinian groups and {$\bold Z$}-lattices.Pac. J. Math. 203 (2002), 395-413. MR 1897906, 10.2140/pjm.2002.203.395 |
| Reference:
|
[3] Kato, K., Kurokawa, N., Saito, T.: Number Theory I. Fermat's Dream.Translations of Mathematical Monographs. Iwanami Series in Modern Mathematics 186 AMS, Providence (2000). MR 1728620 |
| Reference:
|
[4] Kureš, M., Skula, L.: Reduction of matrices over orders of imaginary quadratic fields.Linear Algebra Appl. 435 (2011), 1903-1919. Zbl 1223.15025, MR 2810635 |
| Reference:
|
[5] Maclachlan, C., Reid, A. W.: The Arithmetic of Hyperbolic 3-Manifolds.Graduate Texts in Mathematics 219 Springer, New York (2003). Zbl 1025.57001, MR 1937957 |
| Reference:
|
[6] Voight, J.: Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms.Quadratic and Higher Degree Forms Developments in Mathematics 31 Springer, New York (2013), 255-298 K. Alladi et al. Zbl 1282.11152, MR 3156561 |
| . |
