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Detecting products of elementary matrices in $ {\rm GL}\sb{2}({\bf Z}[\sqrt{d}])$


Author: Randy Tuler
Journal: Proc. Amer. Math. Soc. 89 (1983), 45-48
MSC: Primary 10C30; Secondary 10C02, 10M20, 15A23, 20H25
DOI: https://doi.org/10.1090/S0002-9939-1983-0706508-3
MathSciNet review: 706508
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Abstract: An elementary $ n \times n$ matrix over a ring $ R$ has 1 in each diagonal position and at most one additional nonzero element. Let $ R = {\mathbf{Z}}[\sqrt d ]$ where $ d$ is an integer less than $ - 4$. We give an algorithm for determining whether or not a $ 2 \times 2$ invertible matrix over $ R$ is generated by elementary matrices. This is connected with the theory of integral binary quadratic forms.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0706508-3
Article copyright: © Copyright 1983 American Mathematical Society

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