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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2005 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156607 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-156607 |
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Zabavsky, B. 2019-06-18T17:49:22Z 2019-06-18T17:49:22Z 2005 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 https://nasplib.isofts.kiev.ua/handle/123456789/156607 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. Dedicated to Yu.A. Drozd on the occasion of his 60th birthday en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Diagonalizability theorems for matrices over rings with finite stable range Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Diagonalizability theorems for matrices over rings with finite stable range |
| spellingShingle |
Diagonalizability theorems for matrices over rings with finite stable range Zabavsky, B. |
| 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 |
| author |
Zabavsky, B. |
| author_facet |
Zabavsky, B. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT zabavskyb diagonalizabilitytheoremsformatricesoverringswithfinitestablerange |
| first_indexed |
2025-12-07T13:09:08Z |
| last_indexed |
2025-12-07T13:09:08Z |
| _version_ |
1850855075212165120 |