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 semilo...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/923 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-923 |
|---|---|
| record_format |
ojs |
| spelling |
admjournalluguniveduua-article-9232018-03-21T07:18:38Z Diagonalizability theorems for matrices over rings with finite stable range Zabavsky, Bogdan finite stable range, elementary divisor ring, Hermite ring, ring with elementary reduction of matrices, Bezout ring, minimal prime spectrum 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/923 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/923/452 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-03-21T07:18:38Z |
| collection |
OJS |
| language |
English |
| topic |
finite stable range elementary divisor ring Hermite ring ring with elementary reduction of matrices Bezout ring minimal prime spectrum |
| spellingShingle |
finite stable range elementary divisor ring Hermite ring ring with elementary reduction of matrices Bezout ring minimal prime spectrum Zabavsky, Bogdan Diagonalizability theorems for matrices over rings with finite stable range |
| topic_facet |
finite stable range elementary divisor ring Hermite ring ring with elementary reduction of matrices Bezout ring minimal prime spectrum |
| format |
Article |
| author |
Zabavsky, Bogdan |
| author_facet |
Zabavsky, Bogdan |
| author_sort |
Zabavsky, Bogdan |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/923 |
| work_keys_str_mv |
AT zabavskybogdan diagonalizabilitytheoremsformatricesoverringswithfinitestablerange |
| first_indexed |
2025-12-02T15:33:20Z |
| last_indexed |
2025-12-02T15:33:20Z |
| _version_ |
1850412108823396352 |