Diagonalizability theorems for matrices over rings with finite stable range
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 sem...
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| Дата: | 2005 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156607 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Diagonalizability theorems for matrices over rings with finite stable range / B. Zabavsky // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 151–165. — Бібліогр.: 35 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156607 |
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dspace |
| spelling |
irk-123456789-1566072019-06-19T01:28:05Z Diagonalizability theorems for matrices over rings with finite stable range Zabavsky, B. 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. 2005 Article Diagonalizability theorems for matrices over rings with finite stable range / B. Zabavsky // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 151–165. — Бібліогр.: 35 назв. — англ. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/156607 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Zabavsky, B. |
| spellingShingle |
Zabavsky, B. Diagonalizability theorems for matrices over rings with finite stable range Algebra and Discrete Mathematics |
| author_facet |
Zabavsky, B. |
| author_sort |
Zabavsky, B. |
| title |
Diagonalizability theorems for matrices over rings with finite stable range |
| title_short |
Diagonalizability theorems for matrices over rings with finite stable range |
| title_full |
Diagonalizability theorems for matrices over rings with finite stable range |
| title_fullStr |
Diagonalizability theorems for matrices over rings with finite stable range |
| title_full_unstemmed |
Diagonalizability theorems for matrices over rings with finite stable range |
| title_sort |
diagonalizability theorems for matrices over rings with finite stable range |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156607 |
| citation_txt |
Diagonalizability theorems for matrices over rings with finite stable range / B. Zabavsky // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 151–165. — Бібліогр.: 35 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT zabavskyb diagonalizabilitytheoremsformatricesoverringswithfinitestablerange |
| first_indexed |
2023-05-20T17:50:07Z |
| last_indexed |
2023-05-20T17:50:07Z |
| _version_ |
1796154194735923200 |