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Algebra and Discrete Mathematics, 2005, выпуск 1, страницы 151–165
(Mi adm296)
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Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
RESEARCH ARTICLE
Diagonalizability theorems for matrices over rings with finite stable range
Bogdan Zabavsky Ivan Franko National University of L'viv
Аннотация:
We construct the theory of diagonalizability for matrices over Bezout ring with finite stable range. It is shown that every commutative Bezout ring with compact minimal prime spectrum is Hermite. It is also shown that a principal ideal domain with stable range 1 is Euclidean domain, and every semilocal principal ideal domain is Euclidean domain. It is proved that every matrix over an elementary divisor ring can be reduced to “almost” diagonal matrix by elementary transformations.
Ключевые слова:
finite stable range, elementary divisor ring, Hermite ring, ring with elementary reduction of matrices, Bezout ring, minimal prime spectrum.
Поступила в редакцию: 11.06.2004 Исправленный вариант: 21.03.2005
Образец цитирования:
Bogdan Zabavsky, “Diagonalizability theorems for matrices over rings with finite stable range”, Algebra Discrete Math., 2005, no. 1, 151–165
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm296 https://www.mathnet.ru/rus/adm/y2005/i1/p151
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Страница аннотации: | 254 | PDF полного текста: | 157 | Первая страница: | 1 |
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