Algebra and Discrete Mathematics
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 and Discrete Mathematics, 2019, Volume 27, Issue 1, Pages 1–11 (Mi adm687)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

On hereditary reducibility of 2-monomial matrices over commutative rings

Vitaliy M. Bondarenkoa, Joseph Gildeab, Alexander A. Tylyshchakc, Natalia V. Yurchenkoc

a Institute of Mathematics, Tereshchenkivska str., 3, 01601 Kyiv, Ukraine
b Faculty of Science and Engineering, University of Chester, Thornton Science Park Pool Lane, Ince, CH2 4NU, Chester, UK
c Faculty of Mathematics, Uzhgorod National Univ., Universytetsyka str., 14, 88000 Uzhgorod, Ukraine
Full-text PDF (329 kB) Citations (1)
References:
Abstract: A 2-monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{n-k}\end{smallmatrix}\right)$, $0<k<n$, where $t$ is a non-invertible element of $R$, $\Phi$ the companion matrix to $\lambda^n-1$ and $I_k$ the identity $k\times k$-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility.
Keywords: commutative ring, Jacobson radical, 2-monomial matrix, hereditary reducible matrix, similarity, linear operator, free module.
Funding agency Grant number
National Scholarship Programme of the Slovak Republic
The paper was written during the research stay of the third author at the University of Presov under the National Scholarship Programme of the Slovak Republic.
Received: 10.02.2019
Document Type: Article
MSC: 15B33, 15A30
Language: English
Citation: Vitaliy M. Bondarenko, Joseph Gildea, Alexander A. Tylyshchak, Natalia V. Yurchenko, “On hereditary reducibility of 2-monomial matrices over commutative rings”, Algebra Discrete Math., 27:1 (2019), 1–11
Citation in format AMSBIB
\Bibitem{BonGilTyl19}
\by Vitaliy~M.~Bondarenko, Joseph Gildea, Alexander~A.~Tylyshchak, Natalia~V.~Yurchenko
\paper On hereditary reducibility of 2-monomial matrices over commutative rings
\jour Algebra Discrete Math.
\yr 2019
\vol 27
\issue 1
\pages 1--11
\mathnet{http://mi.mathnet.ru/adm687}
Linking options:
  • https://www.mathnet.ru/eng/adm687
  • https://www.mathnet.ru/eng/adm/v27/i1/p1
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:102
    Full-text PDF :30
    References:18
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024