Detecting products of elementary matrices in $\textrm {GL}_{2}(\textbf {Z}[\sqrt {d}])$
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- by Randy Tuler PDF
- Proc. Amer. Math. Soc. 89 (1983), 45-48 Request permission
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
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Additional Information
- © Copyright 1983 American Mathematical Society
- 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