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Algebra and Discrete Mathematics, 2019, Volume 27, Issue 1, Pages 1–11
(Mi adm687)
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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
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.
Received: 10.02.2019
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
Linking options:
https://www.mathnet.ru/eng/adm687 https://www.mathnet.ru/eng/adm/v27/i1/p1
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Abstract page: | 102 | Full-text PDF : | 30 | References: | 18 |
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