Idempotent factorizations of singular 2 × 2 matrices over quadratic integer rings
Cossu, Laura;
2022-01-01
Abstract
Let D be the ring of integers of a quadratic number field Q[ √ d]. We study the factorizations of 2 × 2 matrices over D into idempotent factors. When d < 0 there exist singular matrices that do not admit idempotent factorizations, due to results by Cohn and by the authors Cozzu and Zanardo. We mainly investigate the case d > 0. We employ Vaseršte˘ın’s result that SL2(D) is generated by elementary matrices, to prove that any 2 × 2 matrix with either a null row or a null column is a product of idempotents. As a consequence, every column-row matrix admits idempotent factorizations.File | Size | Format | |
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Idempotent factorizations of singular 2 2 matrices over quadratic integer rings.pdf Solo gestori archivio
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1.43 MB | Adobe PDF | & nbsp; View / Open Request a copy |
1910.01893v1.pdf open access
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175.41 kB | Adobe PDF | View/Open |
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