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order in an imaginary quadratic field; order in a quaternion algebra; discretely normed ring; isomorphism; primitive algebra
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.
[1] Cohn, P. M.: On the structure of the {$ GL_2$} of a ring. Publ. Math., Inst. Hautes Études Sci. Publ. Math. 30 (1966), 5-53. DOI 10.1007/BF02684355 | MR 0207856
[2] James, D. G.: Quaternion algebras, arithmetic Kleinian groups and {$\bold Z$}-lattices. Pac. J. Math. 203 (2002), 395-413. DOI 10.2140/pjm.2002.203.395 | MR 1897906
[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
[4] Kureš, M., Skula, L.: Reduction of matrices over orders of imaginary quadratic fields. Linear Algebra Appl. 435 (2011), 1903-1919. MR 2810635 | Zbl 1223.15025
[5] Maclachlan, C., Reid, A. W.: The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics 219 Springer, New York (2003). MR 1937957 | Zbl 1025.57001
[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. MR 3156561 | Zbl 1282.11152
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