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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)
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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}
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  • This publication is cited in the following 1 articles:
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    Algebra and Discrete Mathematics
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    Abstract page:105
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    References:19
     
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