Geodesic
On hereditary reducibility of 2-monomial matrices over commutative rings
Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 1-11.

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A 2-monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k0\\0{n-k}\end{smallmatrix}\right)$, $0$, 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, hereditary reducible matrix, similarity, linear operator, free module.
Mots-clés : 2-monomial matrix 
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Vitaliy M. Bondarenko; Joseph Gildea; Alexander A. Tylyshchak; Natalia V. Yurchenko. On hereditary reducibility of 2-monomial matrices over commutative rings. Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a1/

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