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AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Issue no. 3 / 2017 | |||||||
Article: |
UNIQUELY CLEAN 2 X 2 INVERTIBLE INTEGRAL MATRICES. Authors: DORIN ANDRICA, GRIGORE CĂLUGĂREANU. |
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Abstract: DOI: 10.24193/subbmath.2017.3.02 Published Online: 2017-09-30 Published Print: 2017-09-30 pp. 287-293 VIEW PDF While units in any unital ring are strongly clean by definition, which units are uniquely clean, is a far from being simple question, even in particular rings. In this paper, the question is solved for 2 × 2 integral matrices. It turns out that uniquely clean invertible matrices are scarce: only the matrices similar to ![]() The study is split into three cases: the elliptic, the parabolic and the hyperbolic cases, according to the discriminant of their characteristic polynomial. In the first two cases, units are not uniquely clean. Keywords: clean, uniquely clean, class number, Diophantine equation, reduced matrix. Mathematics Subject Classification (2010): 15B36, 16U99, 11D09, 11D45. |
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