RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra Discrete Math., 2013, Volume 16, Issue 2, Pages 171–187 (Mi adm445)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

Reducibility and irreducibility of monomial matrices over commutative rings

V. M. Bondarenkoa, M. Yu. Bortosb, R. F. Dinisc, A. A. Tylyshchakb

a Institute of Mathematics, Tereshchenkivska 3, 01601 Kyiv, Ukraine
b Faculty of Mathematics, Uzhgorod National Univ., Universytetsyka str., 14, 88000 Uzhgorod, Ukraine
c Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko Univ., Volodymyrska str., 64, 01033 Kyiv, Ukraine

Abstract: Let $R$ be a local ring with nonzero Jacobson radical. We study monomial matrices over $R$ of the form
$$ ( \begin{smallmatrix} 0&\ldots&0&t^{s_n}
t^{s_1}&\ldots&0&0
\vdots&\ddots&\vdots&\vdots
0&\ldots&t^{s_{n-1}}&0
\end{smallmatrix} ), $$
and give a criterion for such matrices to be reducible when $n\leq 6$, $s_1\ldots,s_n\in\{0,1\}$ and the radical is a principal ideal with generator $t$. We also show that the criterion does not hold for $n=7$.

Keywords: irreducible matrix, similarity, local ring, Jacobson radical.

Full text: PDF file (252 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 15B33, 15A30
Received: 20.10.2013
Revised: 20.10.2013
Language:

Citation: V. M. Bondarenko, M. Yu. Bortos, R. F. Dinis, A. A. Tylyshchak, “Reducibility and irreducibility of monomial matrices over commutative rings”, Algebra Discrete Math., 16:2 (2013), 171–187

Citation in format AMSBIB
\Bibitem{BonBorDin13}
\by V.~M.~Bondarenko, M.~Yu.~Bortos, R.~F.~Dinis, A.~A.~Tylyshchak
\paper Reducibility and irreducibility of monomial matrices over commutative rings
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 2
\pages 171--187
\mathnet{http://mi.mathnet.ru/adm445}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3186082}


Linking options:
  • http://mi.mathnet.ru/eng/adm445
  • http://mi.mathnet.ru/eng/adm/v16/i2/p171

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vitaliy M. Bondarenko, Maria Yu. Bortos, Ruslana F. Dinis, Alexander A. Tylyshchak, “Indecomposable and irreducible $t$-monomial matrices over commutative rings”, Algebra Discrete Math., 22:1 (2016), 11–20  mathnet  mathscinet
    2. S. V. Sidorov, “On the Similarity of Certain Integer Matrices with Single Eigenvalue over the Ring of Integers”, Math. Notes, 105:5 (2019), 756–762  mathnet  crossref  crossref  isi  elib
  • Algebra and Discrete Mathematics
    Number of views:
    This page:137
    Full text:76
    References:25

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020