• On hereditary reducibility of 2-monomial matrices over commutative rings

      Bondarenko, Vitaliy M.; Gildea, Joe; Tylyshchak, Alexander; Yurchenko, Natalia; Institute of Mathematic, Kyiv; University of Chester; Uzhgorod National University (Taras Shevchenko National University of Luhansk, 2019)
      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 compa\-nion 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.