Abstract
We prove that a commutative Bezout ring is an Hermitian ring if and only if it is a Bezout ring of stable rank 2. It is shown that a noncommutative Bezout ring of stable rank 1 is an Hermitian ring. This implies that a noncommutative semilocal Bezout ring is an Hermitian ring. We prove that the Bezout domain of stable rank 1 with two-element group of units is a ring of elementary divisors if and only if it is a duo-domain.
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Zabavs'kyi, B.V. Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2. Ukrainian Mathematical Journal 55, 665–670 (2003). https://doi.org/10.1023/B:UKMA.0000010166.70532.41
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DOI: https://doi.org/10.1023/B:UKMA.0000010166.70532.41