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Authors: DORIN ANDRICA, GRIGORE CĂLUGĂREANU.
DOI: 10.24193/subbmath.2017.3.02
Published Online: 2017-09-30
Published Print: 2017-09-30
pp. 287-293
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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.
