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Krieg, Aloys

The elementary divisor theory over the Hurwitz order of integral quaternions. (English) Zbl 0663.15003

Linear Multilinear Algebra 21, 325-344 (1987).
The paper deals with the elementary divisor theory over the Hurwitz order of integral quaternions. There exists a diagonal form with certain divisibility conditions for matrices in such circumstances. When the diagonal entries are uniquely determined up to similarity, the matrices are unimodularly equivalent provided that their ranks are greater than one.
Reviewer: R.Ursianu

Cited in 1 Review
Cited in 8 Documents

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A21 Canonical forms, reductions, classification
11R52 Quaternion and other division algebras: arithmetic, zeta functions
11F27 Theta series; Weil representation; theta correspondences

Keywords:

unimodular equivalence; elementary divisor; Hurwitz order; integral quaternions; diagonal form
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References:

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[11] Thompson R. C., Invariant Factors of Integral Quaternion Matrices II · Zbl 0639.15004 · doi:10.1080/03081088708817825
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