On irreducibility of monomial 7 × 7?matrix over local ring
Тип публікації :
Стаття
Дата випуску :
2018
Автор(и) :
Tylyshchak, O. A.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
Випуск :
3
ISSN :
1812-5409
Початкова сторінка :
37
Кінцева сторінка :
44
Цитування :
[APA 7] Tylyshchak, O. A. (2018). On irreducibility of monomial 7 × 7?matrix over local ring. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (3), 37–44. https://doi.org/10.17721/1812-5409.2018/3.5
[ДСТУ] Tylyshchak O. A. On irreducibility of monomial 7 × 7?matrix over local ring. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2018. no. 3. P. 37—44. DOI: 10.17721/1812-5409.2018/3.5 (date of access: 25.07.2026).
We consider a monomial n × n-matrix, which corresponds to a cyclic permutation of the length n, over a commutative local principle ideals ring. Non-zero elements of a non-empty set of first columns of the matrix are identity element of the ring and non-zero elements of non-empty set of the rest columns are a fixed non-zero generator element of the Jacobson radical of the ring. It is known if number of identities or number of generator elements is exact 1 or if n < 7 and number of identities is relatively prime to n, then the matrix is irreducible. If the number of identities is not relatively prime to n, then the matrix is reducible. If the Jacobson radical of the ring is nilpotent of degree 2, then the 7 × 7-matrix of considered form with 3 or 4 identities is reducible. It has been shown that the 7 × 7-matrix is irreducible if the degree of nilpotency of the Jacobson radical of the ring is higher than 2. Some necessary conditions of reducibility of this square matrix of arbitrary size are also established.Key words: monomial matrix, irreducible matrix, 7 × 7-matrix, local ring, principle ideal ring, Jacobson radical.Pages of the article in the issue: 37 - 44Language of the article: Ukrainian
Файл(и) :![Ескіз]()
Вантажиться...
Формат :
Adobe PDF
Розмір :
747.27 KB
Контрольна сума :
(MD5):841baee0078169a92cce25bc6ed9982a
Якщо не вказано інше, ця робота розповсюджується на умовах ліцензії Creative Commons Attribution 4.0 International