Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2
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 Bezo...
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| Дата: | 2003 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2003
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3929 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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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