On hereditary irreducibility of some monomial matrices over local rings


  • A.A. Tylyshchak Uzhhorod National University, 3 Narodna sq., Uzhhorod, Ukraine https://orcid.org/0000-0001-7828-3416
  • M. Demko University of Presov, 1 November 17 str., 08116, Presov, Slovakia


local ring, Jacobson radical, irreducible matrix, monomial matrix, hereditary irreducible matrix
Published online: 2021-06-19


We consider monomial matrices over a commutative local principal ideal ring $R$ of type $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0\,\,&tI_{n-k}\end{smallmatrix}\right)$, $0<k<n$, where $t$ is a generating element of Jacobson radical $J(R)$ of $R$, $\Phi$ is the companion matrix to $\lambda^n-1$ and $I_k$ is the identity $k\times k$ matrix. In this paper, we indicate a criterion of the hereditary irreducibility of $M(t,k,n)$ in the case $t^{\left[\frac{k\cdot(n-k)}{n}\right]+1}\not=0$.

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How to Cite
Tylyshchak, A.; Demko, M. On Hereditary Irreducibility of Some Monomial Matrices over Local Rings. Carpathian Math. Publ. 2021, 13, 127-133.